When I'm looking for a particular image it almost never takes more than about 4 tags to get down to an easily manageable number of pictures to go through. The times when I have to go looking around for stuff is when it turns out that the image in question is undertagged so it doesn't show up from my search - this happens all the time, but having more tags to search with isn't what would help here - it's having the images be tagged better. 6 tags is perfectly sufficient for standard use.
For instance, taking a random picture from my favourites, if looking for post #2833930 I could search sekiya_naru solo fireworks... and get that as the only result.
Let's take something a bit harder - post #2773230. I'm not familiar with touhou so wouldn't recognise the character. If I knew the picture is decently tagged (which I do) then I could search for heart_necklace sun third_eye and get down to 1 image right off the bat with just 3 tags again. Otherwise I'd probably go with hat dutch_angle solo beach :d, which returns 16 results from 5 tags.
I deliberately avoided badly undertagged images for the above examples as these would show how much more tagging wants doing rather than anything else. I also avoided giveaways like images with the artist name on them or images with very prominent but very rare features (like post #2419160 for instance). Otherwise the images were chosen at random.
Remember that if you run out of tags and are looking for a rating:safe image then you can use the safebooru mirror site, which will effectively act as a rating:safe search without using up any of your searches.