Marque 2 manual, see page 5: I trust you're following this step by step, replacing the word "phone" with "Mac", and particularly following the section "Pair Another Phone (= Mac)" since yours was already paired with something?
The "discoverable" status of these headsets can usually not be changed and doesn't need to be, but your Mac's status can... eventually must be "discoverable" for the duration of the pairing.
I think for most BT devices, after it's initially turned on and paired to something, the subsequent times it's turned on it doesn't go into pair mode automatically. Instead, you have to force it into pair mode.
Only when you run the battery t-o-t-a-l-l-y dead. Otherwise your assumption is wrong.
The pairing of headsets with one other BT device lasts until you pair it with another. So, no new pairing required once paired successfully once.
Caution: If you pair it now with the Mac, and after about 2 hours with e.g. a phone, you will need to "re-pair" it with the Mac again if you want to use it with the Mac...