Dog is right, first find the leak.
Before you put water in the kayak, put it on some low sawhorses, or even beach chairs, to support the hull. Water is heavy - 8 lbs to the gallon.
Tilt it slightly backwards and start the aft compartment. If water exits toward the aft end, it's likely the skeg box.
If not, level it and fill it again. If water permeates to the cockpit, it's the rear bulkhead. IIRC it's a foam bulkhead. Over time these flex a lot more than fiberglass bulkheads, so the seal with the side and bottom of the boat is compromised.
To seal a foam bulkhead, clean away the existing sealant w. mineral spirits or pure acetone. Let it dry
Re-seal w. a caulking gun and All Purpose Lexel - the clear sealant. Found at hardware stores. IIRC Ace Hardware has it in stores, or they can order for you. Lexel can be used on wet or dry surfaces. Let it set up.
Note, the skeg box can be a PITA to reach, so you might have to apply the Lexel w. a small wooden spatula (popsicle stick works fine) and do the final smoothing w. your finger. Clean up w. mineral spirits or pure acetone.
I've resealed several bulkheads w. Lexel - for friends - and all of them are now watertight.
One last tip: Do NOT use silicone, it doesn't hold up as well, it's messy, and a PITA to take off before you use something else.