I don't believe figs have a tap root. They have shallow, wide roots that will extend far beyond the drip line.

I don't really know about gophers, but I have recently removed a tree from the ground and can speak to the issues of the roots.

Figs have a fibrous root system with most of the roots on a fig tree are shallow (within 12 inches of the surface). There are a few roots that do go deep, but I would hesitate to call them tap roots. If you surround your tree with a hardware cloth or chicken wire, the roots will grow through and spread (including the one[s] that grow deep into the ground).

You could dig your hole 16" deep and 36" in diameter (approx) and line it with your cage. If the gophers eat the roots outside of the cage, you will have sufficient root mass within the cage to support a decent sized tree. The tree I removed from the ground spent the last year with a 12" deep X 30" moat dug around it without any adverse effects (It actually seemed to do a little better with the root pruning.) Perhaps the gophers can do a little root pruning for you. ;)

I do apologize, I meant to document the removal of this tree (including the root mass under the tree), but my friend with the digital camera had to cancel and I couldn't wait to remove it.

~james