You are playing a 3/4 or 6/8 groove. I would go with 6/8.
Your theme I count as 1 2and3and 4 5 (6) with 6 being your rest.
I would start my search with tap tempo. I have attached a screenshot.
Notice the time signature is set at 6/8 and the tempo is set to 60.
The kick drum is on 1 and 4 and the snare is on 2 3 and 5. 6 is a rest.
I am making the assumption you know how to count 6/8 time.
You may find something is your groove library but odds are you are going to have to create your own.
The 6/8 kick/snare groove is your foundation. Good luck with your search. Or creation.
Dr. Rock
