Hello! First post here and looking for some help.

I purchased my 2002 R50 5-speed a little over a year ago with an extensive packet of service records. The car's only issues thus far have been shift linkage and a misfire due to a bad spark-plug. I replaced all 4 plugs, spark plug wires, central ignition coil, and both shift linkages and upgraded the box with a short-shifter.

The car has been a dream until yesterday, when after being away for 10 days I took the car out for the first time since I got back and at my destination I went to shift into reverse and the shifter kept physically popping out of reverse, not staying engaged. I parked and when I left my destination, I went to shift into 2nd after taking off and the same issue happened; the shifter would pop back into neutral, not allowing the gear to engage. I skipped 2nd and went to 3rd, and when I went to shift into 4th the issue happened yet again. So, I skipped 4th and found that 5th gear engaged fine.

TLDR: While driving, 1st gear, 3rd gear, and 5th gear engage perfectly fine while 2nd gear, 4th gear, and Reverse do not engage. (Once in a blue moon, 4th gear would engage).

After some research, I found that the most likely reason for this issue is the Shift Selector mechanism not functioning as it should. The gears themselves showed no symptoms of failure prior to the other day and as I mentioned before, I replaced the shift linkages recently and if they were faulty, none of the gears would be engaging. I also thought that maybe the physical bushing where the shifter connects into the shift-box was broken, but that wouldn't make sense as all of the gears (other than Reverse) engage and the shifter stays in place while the car is stopped.

Item #1 Is the part I suspect is malfunctioning. Am I right? I don't know enough about the R50 transmission to be sure. Thank you for any insight!
https://new.minimania.com/part/NMD76...i-Cooper-02-04