...With my meter set to ohms,
correct
do I power on the unit
no, and from your pic the transformer isn't connected to pcb, so this wouldn't make much sense anyway
and place negative on chassis ground and positive to each of the contacts?
no. You want to measure resistance (your kind of measurement might measure the rare event of a blown mains transformer shorting to chassis/safety ground) in between -in this case- two spots on pcb.
Am I seeking a particular value to indicate which of the 4 (minus the center) the other two secondaries connect to?
Lets call these 5 spots on pcb 1,2,3,4,5, the center for the transformers center tap connection being 3.
From your "while the one on the left is traced to the hole closer to center. (see pic)" you measure resistance between spot 1 and 2 on pcb. From my previous post these are the same node where one of the transformer secondary outer winding ends connect, so the resistance between 1 and 2 would measure zero ohms. Your assumption says, these spots 1 and 2 are separated, so the measured resistance would be a lot higher than zero ohms (with -from your pic- parts already soldered to pcb, there are other connections already in parallel to these spots, so an infinite resistance of a clean unfitted pcb most likely will not show up). Your assumption further says, spots 2 and 3 are connected, so measure between 2 and 3. Resistance in between would measure zero ohms if your assumption would be correct or a lot higher than zero ohms from my wording.
I'm building for 110V.
so primary windings of your mains transformer would be hooked up in parallel and there will be mains fuse and maybe a mains switch in between your wall outlet and the gssl.
This has nothing to do with transformers secondary connection to pcb.