I know this is a stupid one but I'm pretty OCD and want to make sure that I route the tube like it would have been from the factory. I bought the bike without a battery so I'm not sure how to run the vent tube properly. Thanks in advance!

First up, if you can find a sealed battery to fit, then you won't need the vent tube.

Second, if you do decide to go with a vented battery, then at the back of the Service Manual (see Tech Library) you will find a routing diagram for all wires and cables and I'm pretty sure that the battery vent hose route is shown there.

Might have a bendable tab on the bottom frame cross tube to run it through. Proper original vent pipes generaly have a split close to the start of the pipe where it fits on the battery as a safety valve incase the vent pipe gets blocked with dirt. Only saying 'that' as the split bit goes the battery end not the bottom end.

There might be a decal on the back fender or bottom of the seat pan. The decal shows the route. Yamaha must have thought it important enough to keep the acid off of painted surfaces.

And the chain... a little acid on the chain can cause it to break very quickly. 

Don’t underestimate the importance of that vent tube. The previous owner of my unrestored GT80 installed a new battery and never hooked up a vent tube. Chain guard, brake rods, rear hub, and rear spokes are all acid etched…..

Here is some pics of my crusty 76 DT400 and the battery that was still in it with a 1982 date on it. Can see tube hole on battery which was toward front of bike. Hose is in center of pics.