Before installing software workarounds, check for a small API switch on the controller itself. Many gamepads made at the end of the DirectInput era allow selection between DirectInput and XInput via hardware toggle, a handy option that might not be clearly labeled or readily apparent without careful inspection.
DirectInput-only controllers can stay in the game with x360ce, a freeware utility that translates between APIs and allows systems to recognize older gamepads as Xbox 360 for Windows controllers. Setup isn't complicated but requires separate installation for each title as a replacement XInput.dll, and accompanying configuration files are generated in the folder alongside the game's executable.
Profiles for many older controllers already exist, so custom mapping mostly involves giving functions to the extra buttons or triggers found with gamepads more elaborate than Microsoft's Xbox design. Settings are surprisingly detailed depending on how complex the controller itself is to operate, so be prepared to spend a little time calibrating that wheel and pedal setup before venturing out onto the streets of Los Santos.
Once you’re done, those trusty old Saiteks should be working like new. Just be careful when you rage quit, or you'll be looking at eBay instead of Amazon for replacements. Most of these controllers haven't been made for years, and the closest you'll get to new is unopened old stock.