I am a little bit curious about what sort of tools mods or admins could use that is not available to regular users, and is not privacy sensitive as well. If it is not something that can be shared, I will totally understand that.
By tools, I'm referring to deleted posts that a normal moderator or user can't access (unless created by third party aggregator site), especially when trying to connect an account to another, since deleted posts by moderators could come in handy, IP checks, and various other things. They aren't exactly tools, more like just more access to certain pages. The forum actually has a decent ish alt account detection prompt (exact algorithm unknown), which can be helpful at times. It's by no means an absolute, and it isn't to be treated like X account is linked to Y account, but rather a prompt for further investigation. Its not just that though, a global moderator handling reports in multiple sections, has a higher chance of connecting a post, since if multiple posts of that user is being reported site wide, they might be able to identify the connection easier. I've seen this only on the Altcoin section, since a spammer is usually reported multiple times, and I've caught account farms in this way, and I'm sure a few other moderators have too.
Most accounts that end up getting banned, especially for spam are easily linked. Obviously, they'll be complex examples also, but the vast majority will be for spamming, and spammers usually tend to have more than one account, and write the exact same thing over, and over again without a large amount of variation. Usually, because they're paid or at the very least incentivized to post, and therefore try to churn out as much as possible in a short period of time.
So, I don't have any special access to anything. Admins will have IP records which could potentially be used. Though, obviously we know that's pretty easy to avoid. Though, I think most on the forum know how to avoid IP identification, they just don't for whatever reason especially when it comes to spammers. Probably laziness.
So to recap, while admins or global moderators might not have more tools at their disposable per say, they do have a better chance of linking accounts simply by using the reports as a tool, if you get me. I tend to leave complicated reports in the queue for this reason, if I don't have any additional information to act upon, and there's reasonable doubt, then perhaps someone else looking to handle it will have additional information. Otherwise, the worse thing that happens is no action is taken, and the report goes unhandled or maybe marked as bad if appropriate. Its likely that every moderator that reviewed that report will make a unconscious note though, so if any other reports crop up with the user then that could spark further investigation too.