"So my question is how much time do you spend searching for a possible link when an obvious one is very hard to identify?"
This would be something only you can decide. Personally, I individually look at all 4th to 6th cousin matches and closer. If they have a public tree I try to find the connection and look at shared matches. If they have no tree or a private tree, I look at shared matches.
If no joy there either, I make a note such as 'No connection found. Shared match with xyz' and leave it at that. Sometime in the future I may revisit. It may be that either me or they have come across a brick wall.
''Does that mean the link is more likely to be a maternal one since women changed their surnames and I may simply not have researched back far enough to identify them?"
With 3rd cousin estimate, you only have 16 (perhaps 32) names to compare. With 4th to 6th cousin estimate, you have the potential for 128 5G grandparents (perhaps 256 6G grandparents) to compare.
If either of you have missed out on even one of them, that could be the connectIon, so could be either maternal or paternal.
"Do you assume that because Ancestry has stated a link around the great grand, grand, grand-parents level that it's a definite family match and search accordingly?"
I know exactly how I connect to all 3rd cousin and closer matches, bar one. One 3rd cousin, shared 2G grandparents, has no tree, but using shared matches I have established what I think the connectIon is, but my match does not know names beyond his grandmother. I periodically look for further information about her birth, which does not appear in GRO birth records, but my match does not appear to be very interested in his maternal line.
His grandmother has the surname Smith (which could make searches very difficult!!), but shared matches with several members of Laversuch family lead me to believe that she was daughter of one of the children of Fanny Laversuch who set up family with a John Smith (no marriage found).
So I will always try to connect with a 3rd cousin or closer, and will make an effort even when nothing appears straight away. 4th to 6th cousins are a different matter, I connect positively with the top ones, some of the others I have no idea of the connectIon.
Regards Margaret