[rohrmann]

It probably will not make any difference how you connect. If I were going to set things up for one of those compressors, I would connect a couple of good sized wires to the batteries with a fuse big enough to handle the load of the compressor and run them to a suitable receptacle maybe over to the pass through compartment and wire a plug to the wires of the compressor motor so you aren’t depending on the alligator clips to handle the current.