The most useful weblinks I have come across for finding Toyota Part Numbers are ....
From the links below you need to select from VEHICLE CHARACTERISTICS pickboxes RHD Right Hand Drive For all available model in the UK then select transmission, body type, engine etc.
Can also be used for the MK1 & MK3 by starting at "Select Your Car" and selecting the appropriate options.
UK
Rev1 - http://www.toyodiy.com/parts/q_E_1990_TOYOTA_MR2_SW20.html
Rev2 - http://www.toyodiy.com/parts/q_E_1992_TOYOTA_MR2_SW20.html
Rev3 - http://www.toyodiy.com/parts/q_E_1994_TOYOTA_MR2_SW20.html
Rev4 - http://www.toyodiy.com/parts/q_E_1996_TOYOTA_MR2_SW20.html
Rev5 - http://www.toyodiy.com/parts/q_E_1998_TOYOTA_MR2_SW20.html
JDM
Rev1 - http://www.toyodiy.com/parts/q_J_1990_TOYOTA_MR2_SW20.html
Rev2 - http://www.toyodiy.com/parts/q_J_1992_TOYOTA_MR2_SW20.html click on Market
Rev3 - http://www.toyodiy.com/parts/q_J_1994_TOYOTA_MR2_SW20.html
Rev4 - http://www.toyodiy.com/parts/q_J_1996_TOYOTA_MR2_SW20.html
Rev5- http://www.toyodiy.com/parts/q_J_1998_TOYOTA_MR2_SW20.html
(^appears to cover beams too)
2023 Update
If you cannot see the diagrams on the above website, try this site, it's basically the Toyota EPC with the EPC diagrams
Click on the Europe button to get a drop down menu to select other regions (JDM, USA etc).Then add the year of your car, continue adding info as the buttons appear until you get to the menu that shows all the sections, narrow down your search by selecting the appropriate section. Bear in mind with imports that the year of registration may NOT be the year of manufacture. In this case VIN search is the way to go.
If you enter your VIN into the VIN search you will ensure you get the correct part numbers for your car. If you know the part number you can use that to search and view the diagrams.