The technician and/or the coordinator (meet, meets) with the manager . . .
First, you have to determine if the subject is singular or plural.
“Technician and coordinator” implies that the subject is plural, but “technician or coordinator” implies that it is either one or the other, so the subject would be singular.
(Remember that when you have two subjects joined by ‘or’ or ‘nor,’ you must choose the subject that is nearer to the verb and make that subject agree with the verb.)
So which is it?
The technician and the coordinator meet with the manager . . .
The technician or the coordinator meets with the manager . . .?
Are you still with me?
And/or is a shortcut that can lead to ambiguity or confusion. So-
Avoid using and/or in your writing. Grammar experts agree on this.
If you insist on using ‘and/or,’ I would consider that the ‘or’ is closer to the verb, so I would punctuate the sentence this way: The technician and/or the coordinator meets with the manager.