I believe you can in fact select reverse gear by hand when the trans is in neutral. The detent (pin) comes out of it's bore and locks out reverse when the first/second shift rail are moved even slightly forward or backward.
Of course bear in mind this may not be the problem at all, just an item to pay careful attention to when the trans gets reassembled and the problem fixed. It would be hell to miss that little detent while distracted over some other problem.
It's fairly common for it to 'fall out' during assembly.