I've been to the Ghostgate Shrine while on pilgrimmage - several times - and it takes my soulstone and gives me the quest dialogue but does not flag over the Ghostgate Shrine quest as having been completed. I can't turn in the pilgrimmage until it's completed.
I've tried to use setstage TT_ghostgate 100 and it does not recognize the quest, so not too sure what to do to fix this now.
A second search (not sure why this didn't come up the first time I tried to search) indicated that this might be due to my petty soul gem being full, and that someone had made a soul gem emptier to fix the problem. I used that, returned to the shrine, and got the quest credit.
D'oh! I ended up sacrificing a filled Greater Soul Gem to that fiendish shrine! I'm going to go and desecrate it, now. >:/
Game will not recognize
Game will not recognize Morrowind Commands running under Oblivion Engine.