With poultry shears or kitchen scissors, cut each squab in half through center of breast and back. Pull off and discard fat lumps. Cut off necks and reserve with giblets for other uses. Rinse birds and pat dry.
In a bowl, mix vinegar, honey, and thyme. Add squab and mix to coat with seasonings. Let stand at least 20 minutes or chill, covered, up to 1 day, turning pieces over several times.
Prepare barbecue for indirect heat.
If using charcoal, mound and ignite 60 briquets on the firegrate of a barbecue with a lid (20 to 22 in. wide). When briquets are dotted with gray ash, in about 15 minutes, push equal portions to opposite sides of the firegrate. Place a drip pan between coals. Set the grill in place.
If using a gas barbecue, cover and turn heat to high for about 10 minutes. Adjust burners for indirect cooking (no heat down center) and keep on high. Set a drip pan beneath grill between ignited burners. Set grill in place.
Lift squab from marinade and lay, bones down, in center of grill, not directly over the heat. Cover barbecue and open the vents.
Cook until birds are richly browned, basting squab frequently with marinade, using it all. For rare, breasts are moist and red in center (cut to test); allow about 25 minutes. For medium, cook 6 to 10 minutes longer. Season to taste with salt.