2000 cvpi doesn't engage in reverse all the time

Ok bought a 2000 CVPI with 163K and it drove fine on the test drive. The next time I drove it I could not get it engage in Reverse gear? I let it sit at the house for about 25 minutes, come back out and and it once again grabs Reverse instantly. I have replaced the Range selector and done a transmission pan gasket and new filter. Same problem exists. When it does engage Reverse gear is solid with no slipping or whining or anything. Some days it will work perfectly all day and other day it will come and go with no pattern or warning.

I have a few questions really. 1. Could it be the solenoids not switching onto Reverse?
2. Could the transmission have been replaced at some point with the wrong transmission? I understand there is only one CV LX trans, but the Police Package had 4 different versions and everything externally is the same except for the colors of the plugs going into the transmission. I have read some posts that claim you will have a check engine light and weird shifts if it the incorrect transmission. No check engine lights and yes it is there when you start the car! I called the Ford garage and they were able to tell me that it is a 4R70W but said that they can not give me the codes for the original transmission.