Need Relay with Timer

I am looking for a commercial timer/relay combination that works in the following manner. The output would consist of a relay with normally open contacts.   When 12 volts is applied at the input, the relay would close until the voltage is removed or for 5 seconds, which ever is shorter, i.e., if the voltage was applied for 3 hours the relay would still only be closed for the first 5 seconds, but if the input was present for 3 seconds then the contacts would be closed for 3 seconds. If the input voltage is removed, if even for a fraction of a second, the timer should immediately reset for the next event. Does anyone know of such commercial timer? I thought the Omron 12V H3Y-2 might be the solution but after looking at the timing chart it appears it provides the delay at the beginning of the cycle and not the end.    

You need an interval timer. Omron and other companies have units with multiple operation modes, as well as multiple timing ranges.

Thanks for taking the time to reply. I looked at the suggested offerings from Omron and they all seem to be over $50. After thinking about it a bit, I think if I attach a NC relay to the 12V H3Y-2 output it will reverse the logic and I will have what I want. Since I can obtain both parts on Ebay for less than $10 including shipping, I won’t have wasted a whole of money giving it a whirl even if doesn’t work out. Thanks again.