Why don't I have reverse,? when all the other gears work fine,

You could have a shifter linkage problem. Have you driven off road lately where something might have hit the shift linkage on the transmission? Is the mileage high on the vehicle? Sometimes reverse is the first gear to quit working on a high mileage automatic transmission. If there is nothing broken on the linkage between the gear shifter and the transmission it's probably an internal problem.

If you get underneath the truck, you can check for a broken or bent piece of steel linkage, a damaged cable, or a dent in the pan on the bottom. If you find damage, you can replace the damaged part. If there is a dent in the pan, you can remove it and knock the dent out or replace the pan. If you remove the pan, all the oil will pour out of the transmission. So be prepared to collect it. You need a repair manual to properly reattach a transmission pan. Always use a new gasket/seal. Follow torque specifications and tightening sequence in the manual or it will leak.

Unfortunately, there are no diy repairs inside the housing.

I know you are trying to avoid this, but automatic transmission repair should be done by a certified professional transmission mechanic.