This is correct that once you disconnect the linkage that the internal shift arm could drop into the case. If that happens you may be able to lift it out with a magnet, add a washer, and reconnect. Otherwise the rear the t-case needs to come off.
In your photo you can see the notch in the shift fork. The H-L shift linkage has dropped too low to engage this notch. You probably need a washer on the outside of the case to pull the shift linkage higher so that it will engage the shift fork. You may be able to accomplish this without...