I was able to build the time component while my Sim was living in an apartment in San Myshuno. I was fully expecting to have to move, or at the very least travel away from home, but was desperately using every device in her home first to try to get something to break so she could do the Repair task. For some reason nothing would break for days, and while I was killing time waiting I just idly clicked on the stack of shards in her inventory and tried building the time travel component.
Not sure if there’s supposed to be some animation, but I just got an announcement that she’d built it and it showed up in her inventory.
Successful apartment was 18 Culpepper House, in case that helps anyone else.
