If I was unsure as to where No1 was id do a very quick r/t to the FISO and ask for the position of the aircraft ahead.
If he advises late downwind / on base / turning final etc at least you would know where to look and establish if the traffic you had visual with was him or not.
Always use caution as you have quite rightly demonstrated, but it may save you extending downwind for an aircraft that was actually just transiting pass the zone, rather than flying a not very accurate circuit.
Definately wouldnt turn base though until I was sure that he was already on final and in between me and the numbers.
regards.
