I'll get bashed for saying this, but,
If it leaks, replace it!! Don't use snake-oil, don't be a cheap [censored], just replace the leaky core!
If you really really CBA, at least get the two hoses that feed the core and link them together - NEVER EVER put 'stop leak' products anywhere in your car.
Mechanics fix problems
Cheapskate idiots put bandages over symptoms.