I'm not sure I'd go the route of an alarm after the bilge pump runs "for a few minutes". You bilge pump is primarily designed to take care of nuisance water and, unless it is a pretty good leak, it will only run for a few seconds and then shut off and start up again for a few seconds and cycle. If you have it set for an alarm based on time, there is a good chance you could have a small constant leak that will still not cause the pump to run for an extended lone time (minutes.)
My suggestion:
1. Install a bilge counter that "counts" every time the bilge pump starts, even if it only runs for a few seconds when it starts. You'll get a feel for what is "normal" and then when you see something that is beyond that number of counts you can take action. For my boat, the counter reads 0 even after weeks. If I see 1 or 2 after a couple weeks I probably wouldn't be too concerned but if I see 20 then something is wrong.
2. If you really want an alarm, you can buy one that you install a few inches above your "normal" bilge water level that will then tell you your bilge pump is not working or you have a really big leak that is beyond the capacity of your bilge pump.
The Bilge Counter is a valuable tool. Unless you have a completely dry bilge, when you get to your boat after a few days or weeks away and see water in the bilge, you don't really know if you have a leak or not since you won't know how many times the bilge pump had to run to keep it at that level.
Just my 2 cents.