The panel will still be providing power directly to the fence.

If I interpret the documentation for the charge controller correctly (and I have take only the most superficial glance at it,) the only disadvantage to connecting the fence directly to the battery, rather than to the "load" terminals of the controller, is that you will be bypassing the controller's built-in battery protection circuits. Eg: the controller seems to incorporate a low-voltage cutoff, to protect the battery against being pulled all the way down to 100% discharge by the load.

Thanks Joe - I looked on their site for documentation and couldn't find any. Not sure how I missed it. Anyway, I think I'll try bypassing it and see how it goes. Every day the controller flashes indicating 100% charge so I really don't think the antenna is drawing much juice at all when the door is closed, and then fence shouldn't either, so I'll probably be ok.

Well, when I say"documentation" I'm referring just to the text and pictures on that one web page. That, along with a general knowledge of how this stuff normally works, and I drew some conclusions.

The antenna itself will only draw power when moving, and the timer will draw only a microscopic amount of power at all times.

If terminal space is the concern, I'd suggest moving the timer/antenna connections to the battery, and connect the fence to the load terminals of the charge controller. The fence is much more likely to draw down the battery, so this will offer you maximum protection.

Joe, next time you're down this way I owe you a couple dozen eggs.