I have seen this before, not with a watchman, but IIRC it was a Syphonic Minni TV, and it was a filter cap that was weak. Are you using a original Sony adaptor?
Some adaptors have very little filtering and this could be the problem. If the ripple goes away on battery power you can be certain it's a filtering issue.
There is one cap that might be weak inside the TV and I marked it.
Another thing you could try is a capacitor across the power out of the adaptor.
1000 to 2200 UF 16 volt and see if the ripple goes away.