Cannot comment on whether or not a safety switch is required or not in your installation as I cannot see it.
Others may be able to comment as to why the safety device needs power to reset because, as I mentioned before, never seen this type used for domestic use.
I still cannot see the purpose of your requirement though.
As for a timer to bypass, it would have to connect your 40w bulb to the inverter output via a relay and the relay activated via a 12v timer circuit as your 120v is not available at any beginning instant if you follow my drift. Then again if the relay is nc then I would still go with the 12v control anyway.
Therefore probably a basic delay on timer from Ebay for a few dollars would do the job.
http://www.ebay.com.au/itm/DC-5V-12...hash=item3ae6b3f9fe:m:mNB8XqeeqL8F4cHAC_y5TDA