Or Jacobi hadn't used the fob watch to hide his Master persona yet. Wouldn't that be far, far simpler?
Yeah, although I think (not completely sure on this one) he reveals in Utopia that he was found as a naked child on the shores of something or another, and that he had already lost his memory at that point. I think the implication was that he used the fob watch just before or during his regeneration (which might also explain why he regenerated into a child, which doesn't seem to be the usual process - although it's always weird with the Master).
I'm not 100% on that though, it's been a while since I've seen that episode.
Edit: Found it:
Professor Yana: Time and time and time again, always running out on me.
Martha Jones: [looking at his watch nervously] Can I have a look at that?
Professor Yana: Oh, it's only an old relic. Like me.
Martha Jones: Where did you get it?
Professor Yana: I was found with it.
Martha Jones: What do you mean?
Professor Yana: An orphan in the storm. I was a naked child found on the coast of the Silver Devestation. Abandoned with only this.
Martha Jones: Have you ever opened it?
Professor Yana: Why would I? It's broken.
Martha Jones: How do you know it's broken if you've never opened it?
Professor Yana: It's stuck. It's old. It's not meant to be. I don't know.
[Martha turns the watch over. The same alien writing as the Doctor's is on it]
Professor Yana: [suspiciously] Does it matter?
Martha Jones: No... it's... nothing. Listen, everything's fine up here. I'm going to see if The Doctor needs me.
[runs out in a panic]