Terry,
Interesting thought! I presume you refer to the "traditional" over-and-under vented type of tank? I'll go with that presumption, for now...
It shouldn't be necessary to connect to both vent tubes. Just cap the filler tube. The overflow tube should be sufficient. It is the first one to "uncover" into "air" space in the tank as fuel is used up. And it isn't much later in the flight that the other tube also uncovers into air space - i.e., is no longer under the fuel surface inside the tank.
That is useful since there may be a stand-pipe pressure* in, say the uniflow, vent tube that leads to a pulsing and bubbles from muffler pressurizing the tank through it. I've had some engines and planes where muffler pressure to the uniflow tip didn't run well, but switching to the overflow vent did run very well.
* - Liquids seek the same level in an open tube partially submerged in a container, as the rest of the liquid. With the angles of the loads on the fuel in flight, the 'fuel surface' tries to climb quite a bit up the uniflow vent tube. Outside air pressure, whether atmospheric, ram air, or muffler pressure, has to push past the fuel 'standing' in the uniflow tube to be released inside to replace the fuel the engine draws out. Glow engines don't much mind any bubbling that results, except, as mentioned, I've had a few that worked better with pressure to the tube that didn't end under the fuel surface. Diesels are more finicky, with their low vapor pressure, the heat and vibration - they will squirt fuel out a uniflow vent!
The reason that the muffler pressure works and a single vented - free vented - tank doesn't is that the pressure compensates for the change in fuel "head" - the height above the fuel pickup tube, under the load angles and conditions in flight. That height change would otherwise make a lot of difference in the engine run from tank full to empty.