Just to be a wee bit picky, does the shotgun in question have one or two triggers? Can you select which barrel fires first?

If you've got two triggers, the tests above should prove if the firing pin springs/hammer springs are still good. If the firing system has inertial mechanisms to enable the second barrel, the primers aren't enough to set the second firing mechanism. In that case, you'd have to test one barrel, break the shotgun to cock the hammers, select the other barrel to fire first and then test that barrel.

Leaving the gun cocked and loaded for 25 years certainly isn't best practice.