1996 toyato dyna engine light comes on when put in to reverse
Hello and welcome to JustAnswer!
I see that your question has been up for an extended time without a response and while this vehicle would not be in my area of greatest expertise I would like to help.
The first step in diagnosing the problem is to connect a scan tool and see what fault codes are stored in the engine and transmission control modules. The engine light comes on because one of the modules has seen a problem somewhere in a monitored system or component and sets a fault code. There are dozens of possible fault codes and for each of them there are dozens of possible causes.
If the problem happens reliably and only when putting it into reverse then I suspect the problem is either in the transmission or you have a wiring issue, if I knew what codes were setting I would be able to have a much better idea. It is possible that the transmission is slipping enough only in reverse that a gear ratio error fault code is setting. It could also be an issue with the transmission range sensor.
The problem may also be happening because a wire is being pinched or is rubbing when you put it in reverse. Putting it in reverse moves the powertrain forward and this may be enough movement to cause a wire to short to ground or an intermittent break to open up somewhere.