Oof... old school indeed. My first thought is to put it in a museum and buy a new one, unless you can get inside and make sure the contacts are clean.
It doesn't necessarily have to be near the battery as long as it's near the battery CABLE -- i.e., the less you have to extend the battery cables, the better. A marginal electrical system will have a heck of a time if you add 5 to 10 feet of battery cable. If the switch is low-quality or has corroded or burned contacts, forget it. But since the battery is basically right on the other side of the dash, I don't think the extra cable would be a problem.
My TR3 has one of those green knob cutoffs (unscrew the knob to disconnect) that gets mounted directly on the battery post. It's more for long-term storage or anti-theft, not much use in an emergency, but it added nothing to the cable run.
Another of mine has a racing kill switch, unfortunately under the car in such a position that you have to shimmy your entire torso under to reach it... again, useless in an emergency.
One of Dad's cars had a racing kill switch mounted at the base of the seat (very close to the battery, which was under the seat). Perfect spot for emergencies, convenient for long-term storage, and hidden just enough that it probably would have been effective for anti-theft.
All three above had the switch located so the battery cable didn't have to be extended or looped around.
So the ideal location is close enough to reach in an emergency, hidden enough that a thief might not see it easily, and near where the battery cable is already. Under the dash seems like a pretty good spot, just not the most convenient.
But lucky you, there's a hole in the handle which is meant to take a lanyard or pull cable for remote operation. Mount the switch out of the way under the dash and add a simple pull cable, routed a little closer to where you can reach it (like taped to the back of the dash, maybe). Or maybe use a choke cable and mount the pull knob in plain sight. If a thief thinks he's got to pull it to get the car started, he will just be disconnecting the battery!
Oh, and -- don't EVER try to stop the car by turning off that switch (except in a real emergency). The contacts are (generally) designed for continuous duty, but the voltage spike that occurs when you break contact while current is flowing will burn the contacts. A typical kill switch can handle 100+ Amps and work for some thousand actuations, but using it to turn off the car will wreck it in about a dozen attempts.