Sump Alarm - need 120VAC Latching Relay Circuit

Guess I'm not sure exactly what you want. I get the 'latching relay' part, but you say the only ones you can find are 'plug in' types. I would tend to use a plug in type as it would be easy to pull out and replace in the future. You could just get the appropriate base and convert plug in to screw terminals if you don't want to solder. Or if you do want to solder, I guess you could just solder to the relay pins and use some heat shrink tubing to insulate the pins. But if the relay ever fails, you're in for a job to replace it.

If you're not wanting to use a latching relay, I suppose two normal relays in a 'back-to-back' configuration would latch on, then you could have a manual reset which would cut power and reset the circuit. I suppose you could also take a relay with a coil of the same voltage you intend to drive, then run a wire from the output back to the coil, so it would be self energizing. The trouble with these is if you loose power, the relay's will reset where the true latching relay should stay latched until specifically reset.

You can use a couple relays, one single and the second DPDT. First parallel the SPDT relay to your pump so that you get a clean contact whenever the pump fires. Use this relay to fire the 2nd relay. one side of the relay is to make/break the strobe circuit, and the other side is parallel to the 2nd relay input, so when the pump goes off the relay will stay latched. You can do it only one relay but you'd need a diode to keep from backfeeding to the pump.

Parallel relay #1 with the pump so the first relay trips whenever the pump is active. Loop the hot feed for the 2nd relay through the common/normally open contact of the 1st relay, so when the pump fires the first relay triggers the 2nd relay.

2nd relay: 1st contract will make/break strobe circuit wire your hot leg for the strobe through the common/normally open so when the second relay is fired your strobe gets a complete circuit. Now, in order to get the relay to latch you will oop the hot feed for the 2nd relay power through the common/normally open terminals of the second contact on relay #2, so when this relay is fired it pushes power to the relay's hot input and therefore will latch untill that power is removed (manually reset). Your power for this contact has to be the same circuit as the one you're using to power the 2nd relay, and has to be constant (before the pump control).