Thanks!
I have taken a closer look, did about an hour of debugging, but no luck. The override does trigger and the search does return the correct items, but they are not displayed as they should be.
I suspect it is due to how the Divi Machine addition works. I guess it has it’s own loop and it overrides the original, regardless what Ajax Search Pro does. I don’t think there is a way to override that, or at least I couldn’t find it. Some query variables were transfered, but most of them are overwritten, so my guess is that there is a hook beyond the search that’s being overwritten.
As for the product tags, specifically search phrase “2448”: The way the index table gains significant performance is by executing specialized search queries. One of the main rules is, that the matching can not be within the words. So for example “2448” will match “2448HD” but will not match “22448BB5″ – because it does not start nor ends with the search phrase. This is a trade-off for performance and it can’t be avoided, otherwise a non-indexed query would be executed by the database server, which is basically what we want to avoid.
This is why there is a difference. If middle-word matches are very important to you, you should not use the index table engine. Queries on the taxonomy terms (tags) database table are fairly quick, as it has it’s own special index (of a different kind).