I had no clue what you were talking about when you said "forklift" so I googled Menards forklift and got lucky. So we're all on the same page, is this the item in question?
What exactly is this AC-DC converter you have? Is this a Menards wall-wart adapter?
Pending clarification, I think John H above has the solution...sharing AC and DC common. This means no relay required. We can clarify what/how following confirmation of exactly what you have.