Hi Alex, and welcome.
I don't collect vintage Rolex or Panerai, but I've been round long enough to know that parts and service can be tricky. The same applies to the Heuers, it's a web of who to know & trust and who not to. But, once you have a Heuer, it's relatively easy to maintain if you get onto here and explain what's needed. You'll always get pointed in the right direction.

TAG Heuer Switzerland do actually do some grand work, the problem is that it can be a long process, and based on a lot of one sided trust. There isn't the 'back & forth' communication that you want as a vintage collector - you essentially send it off & trust that they do as per your instructions. Problems may occur - ie. the hands may come back relumed, when you asked for the original creamy lume to be not touched, and little things like that.

There are a good bunch of indy people in the US and UK/Europe that can do all that TH can do, and in most cases to an equal or higher standard.
Parts are hard to find, ebay and the trader section of this forum are the best places to find what you're after. But, these 'hardships' are part of the Heuer allure, it's not just a case of buying off the shelf, which makes them special.

There are plenty of us here with multiple Heuers - in fact, most on here have sizable collections, and I reckon non of them have been put off by parts/service issues.

Golden rule: If you do get one - get on here first before handing it over to any old watchmaker. It'll save you a headache.
The trader section here has some wonderful watches for sale, and the members of this forum are some of the trusted people I know. Just be careful at the moment though, if you place a 'Want To Buy' ad.. there are a few brainless scammers that are on the loose lately, claiming to "have what you want", you'll probably spot them a mile away, but worth letting you know anyway.

Stewart