There is only the one LED in the base for the BOT EOT sensor, the only other LED is the activity indicator on the front. There a a couple holes that are for screws that come up from underneath. The hole is not right at the end of the tape. When the tape is fully rewound it does not stop right at the hole, it will rewind until it detects the hole and then it moves forward a bit at normal read speed looking for the first record on the tape, if it does not find it within the first few minutes it gives up and stops so for a fully rewound tape the hole will beyond the position the tape stops at towards the spool with less tape on it, but be careful moving the tape by hand, if you move the hole past the sensor toward the spool with the most tape the next time you insert the tape it will despool.
The other common problem with these drives is the "tire" on the capstan was made of of a compound that breaks down over time, so if it has not been replaced in your machine it is likely that it has fallen apart and is unable to drive the tape if you search on the web you will find some suggestions on how to rebuild this.
As I mentioned any of the original HP cartridges that are still around will be quite old now and another thing that happens with them is if they have been sitting for a long time without the tape moving, the pressure of the drive band on the tape may cause the oxide layer to bond to the back of the tape on top of it and when you move the tape it tears a spot of oxide off which makes the tape useless. I suppose that could be fixed by clipping off the damaged portion and making a new end of tape hole the appropriate distance from the end, but I have not tried this.
I don't use my 85A much since I got a 86B and a HPIB dual diskette unit. I think that for the little slow storage the tape drive offers, it is not worth all the trouble to get them working. Some people have also modified the drives to use newer cartridges, but I think that if you just need storage HPIB diskette or even the HPDrive disk emulation over HPIB is a much better solution.