E30 Zone

Bringing a '87 325is back to life and finding that it won't go into reverse....not even the "notch" for the gear. All other gears shift very well.

The linkage and bushings look beat up so I will be replacing the complete set up with an IE short shift kit in the hopes that remedies the problem.

What could it be otherwise...broken teeth in the gearbox?

The problem is likely to be the worn linkage. The other likely possibility is a dragging clutch, depending on the exact symptoms you have.
Replace the linkage with OE parts, possibly using a 1.9 Z3 gear lever, not aftermarket junk.

It is likely too late to give you the most possible cause and solution.
If you still need it let me know.
Goris