Hiya!
I’ve just had a look at that by playing with the search over here on inSpired and I can kind of see what you mean there. The Tags that show up as search suggestions are mainly intended to act as filters and are generated by the system based on what it thinks are relevant to the search. I believe it also adapts based on the tags that have been applied to threads as well. Selecting any tag will filter out everything that doesn’t have that tag in it.
Given that a huge number of tags can exist though, showing them all isn’t always possible, so the tags that don’t appear on any thread in the search results at all are hidden away to reduce clutter. The best way to make sure relevant tags appear is to try to make sure threads are tagged appropriately, otherwise the tag you’re after might never show up. The search feature is designed to learn and adapt over time in order to improve accuracy, but it does need some help to make sure that it knows what you’re after.
If the thread you’re after doesn’t have any tags at all, then I’m afraid there won’t be any tags to search with for it. 