Another case of hidden screws. Because these are the sorts of things that slowed me up in the past, when I come across one (and when I remember to photograph it), I'll pass it on and hopefully help others in the future.
The original Taylor Expression System used a pair of AA batteries. Usually, these are problem free but, sometimes, a battery can get stuck in its housing. Grrr.
It's possible to use a paperclip to poke it out from inside the guitar but this is massively fiddly. There's usually a small hole that'll accept an unbent paperclip so give it a go. If it's not a runner (probably not), you might have to remove the jack/power module to get better access.
At first glance, it's a mystery operation but, it's not too bad when you know about the secret screws.
Remove a Taylor Expression System Jack Module
Unscrew the strap button from the endpin jack.
Using an Exacto knife, or similar, prise the plastic cover from the face of the module. It should come off quite easily. Check out the photo below — it explains it better than words can.
Try not to touch the gummy adhesive because there's a good chance it'll be sticky enough to reattach when you're done.
Unscrew the screws and carefully slide out the power/jack module. And when I say 'carefully', I mean very carefully. The flat cable that connects the jack to the preamp is probably tied to one of the body sensor cables. Make sure that removing the jack module doesn't pull on the body sensor cable as it's easy to damage it. Again the photo below should show what I mean.
If you need some slack, you can (fairly) easily unplug the RJ-45 (network style) plug from the jack module by reaching through the soundhole and depressing its little latching tab.
This info applies to the older Expression System that used the AA batteries. The newer version (ES2) uses a 9V battery. It doesn't tend to have these issues and doesn't have secret screws.
NOTE: The internal image above is from a Taylor guitar with a 'broken' power module. The rear battery contact and housing has come detached. You probably shouldn't see the end of the battery on your own guitar.