After a bit of digging, I have partially answered my own question. There are two places where the products a standalone app requires are listed:
- The output of compiler.build.standaloneApplication
- In the standalone app's root directory in file requiredMCRProducts.txt.
For my application, I found (1) and (2) listed different products, and I needed to include all of them for the application to run. The file in (2) just lists product numbers. These are linked to product names files in the MATLAB Runtime installer's productData subdirectory. These are given in the table below, with a corresponding instruction line. 
Once the required products are identified, MATLAB Runtime can be installed selectively using the -inputFile argument when running MATLAB Runtime install. The input file should include the instruction lines from the table and any other necessary arguments. For an example input file, please see my other question.
This method works in MATLAB R2021a. It does not work in R2019b. Perhaps a Mathworks staff member can confirm when the selective install function was added. I suspect it came along with the ability to package standalone applications into Docker images in R2020b. https://uk.mathworks.com/help/compiler/release-notes.html
Table linking product numbers to input file instruction lines. Used commented code because I couldn't figure out how to insert a table.
%productNumber	productName														instruction
%35000			MATLAB Runtime - Core											product.MATLAB_Runtime___Core true
%35010			MATLAB Runtime - Numerics										product.MATLAB_Runtime___Numerics true
%35051			MATLAB Runtime - NET And Excel Addin							product.MATLAB_Runtime___NET_And_Excel_Addin true
%35052			MATLAB Runtime - Hadoop And Spark Addin							product.MATLAB_Runtime___Hadoop_And_Spark_Addin true
%35053			MATLAB Runtime - Java Addin										product.MATLAB_Runtime___Java_Addin true
%35054			MATLAB Runtime - Production Server Addin						product.MATLAB_Runtime___Production_Server_Addin true
%35055			MATLAB Runtime - Python											product.MATLAB_Runtime___Python true
%35103			MATLAB Runtime - Control System Toolbox Addin					product.MATLAB_Runtime___Control_System_Toolbox_Addin true
%35104			MATLAB Runtime - System Identification Toolbox Addin			product.MATLAB_Runtime___System_Identification_Toolbox_Addin true
%35106			MATLAB Runtime - Optimization Toolbox Addin						product.MATLAB_Runtime___Optimization_Toolbox_Addin true
%35108			MATLAB Runtime - Signal Processing Toolbox Addin				product.MATLAB_Runtime___Signal_Processing_Toolbox_Addin true
%35111			MATLAB Runtime - Mapping Toolbox Addin							product.MATLAB_Runtime___Mapping_Toolbox_Addin true
%35112			MATLAB Runtime - Deep Learning Toolbox Addin					product.MATLAB_Runtime___Deep_Learning_Toolbox_Addin true
%35117			MATLAB Runtime - Image Processing Toolbox Addin					product.MATLAB_Runtime___Image_Processing_Toolbox_Addin true
%35119			MATLAB Runtime - Statistics and Machine Learning Toolbox Addin	product.MATLAB_Runtime___Statistics_and_Machine_Learning_Toolbox_Addin true
%35122			MATLAB Runtime - Model Predictive Control Toolbox Addin			product.MATLAB_Runtime___Model_Predictive_Control_Toolbox_Addin true
%35123			MATLAB Runtime - Fuzzy Logic Toolbox Addin						product.MATLAB_Runtime___Fuzzy_Logic_Toolbox_Addin true
%35124			MATLAB Runtime - DSP System Toolbox Addin						product.MATLAB_Runtime___DSP_System_Toolbox_Addin true
%35130			MATLAB Runtime - Financial Toolbox Addin						product.MATLAB_Runtime___Financial_Toolbox_Addin true
%35131			MATLAB Runtime - Partial Differential Equation Toolbox Addin	product.MATLAB_Runtime___Partial_Differential_Equation_Toolbox_Addin true
%35135			MATLAB Runtime - Wavelet Toolbox Addin							product.MATLAB_Runtime___Wavelet_Toolbox_Addin true
%35136			MATLAB Runtime - Communications Toolbox Addin					product.MATLAB_Runtime___Communications_Toolbox_Addin true
%35141			MATLAB Runtime - Database Toolbox Addin							product.MATLAB_Runtime___Database_Toolbox_Addin true
%35144			MATLAB Runtime - MATLAB Report Generator Addin					product.MATLAB_Runtime___MATLAB_Report_Generator_Addin true
%35150			MATLAB Runtime - Datafeed Toolbox Addin							product.MATLAB_Runtime___Datafeed_Toolbox_Addin true
%35160			MATLAB Runtime - Curve Fitting Toolbox Addin					product.MATLAB_Runtime___Curve_Fitting_Toolbox_Addin true
%35162			MATLAB Runtime - Instrument Control Toolbox Addin				product.MATLAB_Runtime___Instrument_Control_Toolbox_Addin true
%35166			MATLAB Runtime - Simulink 3D Animation Addin					product.MATLAB_Runtime___Simulink_3D_Animation_Addin true
%35178			MATLAB Runtime - Image Acquisition Toolbox Addin				product.MATLAB_Runtime___Image_Acquisition_Toolbox_Addin true
%35180			MATLAB Runtime - Parallel Computing Toolbox Cluster Addin		product.MATLAB_Runtime___Parallel_Computing_Toolbox_Cluster_Addin true
%35183			MATLAB Runtime - Bioinformatics Toolbox Addin					product.MATLAB_Runtime___Bioinformatics_Toolbox_Addin true
%35186			MATLAB Runtime - RF Toolbox Addin								product.MATLAB_Runtime___RF_Toolbox_Addin true
%35190			MATLAB Runtime - Global Optimization Toolbox Addin				product.MATLAB_Runtime___Global_Optimization_Toolbox_Addin true
%35191			MATLAB Runtime - Fixed-Point Designer Addin						product.MATLAB_Runtime___Fixed_Point_Designer_Addin true
%35196			MATLAB Runtime - Computer Vision Toolbox Addin					product.MATLAB_Runtime___Computer_Vision_Toolbox_Addin true
%35203			MATLAB Runtime - SimBiology Addin								product.MATLAB_Runtime___SimBiology_Addin true
%35208			MATLAB Runtime - Aerospace Toolbox Addin						product.MATLAB_Runtime___Aerospace_Toolbox_Addin true
%35212			MATLAB Runtime - Phased Array System Toolbox Addin				product.MATLAB_Runtime___Phased_Array_System_Toolbox_Addin true
%35224			MATLAB Runtime - Vehicle Network Toolbox Addin					product.MATLAB_Runtime___Vehicle_Network_Toolbox_Addin true
%35225			MATLAB Runtime - Econometrics Toolbox Addin						product.MATLAB_Runtime___Econometrics_Toolbox_Addin true
%35227			MATLAB Runtime - Simulink Design Optimization Addin				product.MATLAB_Runtime___Simulink_Design_Optimization_Addin true
%35236			MATLAB Runtime - Financial Instruments Toolbox Addin			product.MATLAB_Runtime___Financial_Instruments_Toolbox_Addin true
%35240			MATLAB Runtime - LTE Toolbox Addin								product.MATLAB_Runtime___LTE_Toolbox_Addin true
%35242			MATLAB Runtime - Robotics System Toolbox Addin					product.MATLAB_Runtime___Robotics_System_Toolbox_Addin true
%35245			MATLAB Runtime - WLAN Toolbox Addin								product.MATLAB_Runtime___WLAN_Toolbox_Addin true
%35250			MATLAB Runtime - Risk Management Toolbox Addin					product.MATLAB_Runtime___Risk_Management_Toolbox_Addin true
%35251			MATLAB Runtime - Audio Toolbox Addin							product.MATLAB_Runtime___Audio_Toolbox_Addin true
%35252			MATLAB Runtime - Automated Driving Toolbox Addin				product.MATLAB_Runtime___Automated_Driving_Toolbox_Addin true
%35256			MATLAB Runtime - Text Analytics Toolbox Addin					product.MATLAB_Runtime___Text_Analytics_Toolbox_Addin true
%35257			MATLAB Runtime - Sensor Fusion and Tracking Toolbox Addin		product.MATLAB_Runtime___Sensor_Fusion_and_Tracking_Toolbox_Addin true
%35258			MATLAB Runtime - Predictive Maintenance Toolbox Addin			product.MATLAB_Runtime___Predictive_Maintenance_Toolbox_Addin true
%35261			MATLAB Runtime - 5G Toolbox Addin								product.MATLAB_Runtime___5G_Toolbox_Addin true
%35272			MATLAB Runtime - Reinforcement Learning Toolbox Addin			product.MATLAB_Runtime___Reinforcement_Learning_Toolbox_Addin true
%35274			MATLAB Runtime - Rapid Accelerator								product.MATLAB_Runtime___Rapid_Accelerator true
%35275			MATLAB Runtime - ROS Toolbox Addin								product.MATLAB_Runtime___ROS_Toolbox_Addin true
%35276			MATLAB Runtime - Navigation Toolbox Addin						product.MATLAB_Runtime___Navigation_Toolbox_Addin true
%35278			MATLAB Runtime - Lidar Toolbox Addin							product.MATLAB_Runtime___Lidar_Toolbox_Addin true
%35281			MATLAB Runtime - Radar Toolbox Addin							product.MATLAB_Runtime___Radar_Toolbox_Addin true
%35282			MATLAB Runtime - UAV Toolbox Addin								product.MATLAB_Runtime___UAV_Toolbox_Addin true
%35380			MATLAB Runtime - Parallel Computing Toolbox GPU Addin			product.MATLAB_Runtime___Parallel_Computing_Toolbox_GPU_Addin true
%35500			MATLAB Runtime - Web Apps Addin									product.MATLAB_Runtime___Web_Apps_Addin true






