Adventurenick, thanks for the response.
I may have been wrong all along. I think link localizer is working even with W3 Total Cache activated. I may have been misled the whole time because when I tested it with the cache on either I got one of those odd proxies that doesn’t work for the test or I didn’t wait long enough for everything to load before seeing if the links changed. So I thought it didn’t work. Then when I deactivated the cache it seemed to work so I thought that was the problem. But it may have just been a fluke thing in the first place.
Anyway, at this point it seems to work with W3 Total Cache.
I was going to set the cache not to minify the Affiliate Link Localizer js file as you said, Nick, just to be sure. But when I went into the settings there was no place to name specific js files to exclude. That’s probably because this site is on an older version of WP with an older version of W3. Perhaps in newer versions of W3 there is a place to exclude specific js files. I tried to upgrade W3 and that just led to all kinds of problems. So I had to put it back to the old version of W3.
At this point, I am pretty sure W3 is running and the link localizer is also working.