I personally experienced 2 TA's, on one I've never seen the intruder despite looking out and not IMC and on the second one we saw the intruder at the very last time (it was a light piston-twin) and it was also IMC,
these to say that:
1- According SOP's we must follow any TA
2- It is nice to look outside, but as you know, sometimes it's very hard to pick an aircraft doing the approach just in front of you!
3- It is working only if every body do the same ( look at Bodensee)
Mayday vs Pan Pan:
When dealing with a threatening failure, engine, flight control, structural damage, smoke-fire) one is flying, navigating and radioing, the other is doing the MC's, then we should return to normal loop (extended) and assess the situation? right, then you choose to decalre an emergency perhaps with the mandatory reports, 7700 and TA only, so it is likely that you started to descend a bit already! Not easy when under pressure to think at all those things together and not missing a part...
Cheers