Here is something that might work for you. It is based on either two 555s or one 556 chip.
You specified that the inputs Set~ and Clr~ are active low, such as would happen if you used a clip lead to ground. That is what the switches in the dashed box simulate.
The first 555 is used as a latch (flip-flop). It debounces the inputs and "remembers" that a Set~ pulse has happened, and it starts the delay period of ~2s. When the RC network charges to 2/3 of 12V (8V), the second 555 output goes low, pulling in the load relay. It stays pulled in until the Clr~ pulse goes low.
I made it such that it is the negative going edge of Set~ that starts the timer, and it doesn't matter how wide the Set~ pulse is. It can be very short and end before the 2second delay, or it can even be longer than the 2 second delay period.
Note the traces. The down-edge of the green trace V(set~) starts the 2 second delay. When the blue trace reaches 8V, the purple trace I(L1) shows the current through the relay coil as it pulls-in. When the red trace V(clr~) goes low, that resets the timing network and drops out the relay.
The delay period is proportional to the product of R3 and C1 ( 180000χ10e-6 = 1.8s). You can make it more or less as needed.