[Dainton]

You're registering the right events, but your onevent is mixed up.

AI1:SetScript("OnEvent", function(self, event, ...)
    if event == "UNIT_VEHICLE_ENTERED" then
        AI1:SetBackdrop({bgFile = "Interface\\AddOns\\AI-Suite\\Art\\V1.tga"})
    elseif event == "UNIT_VEHCILE_EXITED" then
        AI1:SetBackdrop({bgFile = "Interface\\AddOns\\AI-Suite\\Art\\A1.tga"})
	else
		AI1:SetBackdrop({bgFile = "Interface\\AddOns\\AI-Suite\\Art\\A1.tga"}) -- backup
	end
end)

Change them to UNIT_ENTERED_VEHICLE and UNIT_EXITED_VEHICLE.