Im working on a 2009 hyundai accent, it came to me with a no crank issue. replaced neutral safety swtch still no crank. finally found the issue where an old car lot installed a starter interrupter gps and the crappy wire connectors they used came apart. reconnected the wires fired right up. cool thats fixed. Go to put it in reverse it wont move, moves in D, 2 and L but jerks into gear. I revved the engine while in reverse and shut the key off and it jumped into gear and moved. It only starts in park and neutral like its supposed to so i feel like the switch isnt the issue but moving in reverse as i shut it off in gear tells me some sort of electrical issue. Any ideas?

 

There is a particular procedure to install and adjust the neutral safety sw. I suspect it is not adjusted correctly. Also we don't know if there was any corrosion inside the plug.
Unfortunately, this all has to be checked out and verify all was done correctly.