1. Go on vacation.
2. Go on a vacation.
3. Go on the vacation.
4. Go on vacations.
5. Go on the vacations.
Are they all grammatical?
Americans "go on vacation" while many other people "go on holiday."
I can be home from work and sitting on my deck reading a book while I'm "on vacation" but I wouldn't say I was "on A vacation."
Going on A vacation implies travel.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.