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