NO expert BUT being a brass fitting/tube wouldn't it be a "NPT" or a National Pipe Thread because "Machine" threads do not "seal" so you couldn't seal the "vacuum" with a machine thread!!! MY "guess" would be a 1/8th NPT or 1/8 National Tapered Pipe Thread!!! AS I said....MY GUESS
If you've stripped it, you could go 1/8 NPT and use an adaptor to get back to 3/16 tube.