The skill applies to "one heavy infantry support system listed in the back of this book". Thus, the skill covers weapons operated by members of the infantry branch, while FA Gunnery would cover artillery systems operated by artillerymen.
Pg. 38 of Mercenary covers "Support Weapons" and states that these weapons require Heavy Weapons skill:
SLUG THROWERS
Light Assault Gun
Light Machinegun
Autocannon
VRF Gauss Gun
GRENADE LAUNCHERS
Early Grenade Launcher
RAM Grenade Launcher
RAM Auto Grenade Launcher
But the skill description explicitly includes Mortars, so they're obviously Heavy Weapons. Since there's no specific skill listed for Tac Missiles, and since Tac Missiles are commonly used by infantrymen, it's reasonable to include them in Heavy Weapons.
In the case of mortars, there's a little overlap. Artillerymen might well operate mortars (especially heavy mortars), so I'd treat the Mortar skill as available for recipients of either the FA Gunnery skill or the Heavy Weapons skill.
For lower tech armies (TL7-10), I'd allow Mortar or Tac Missile skill to the recipient of FA Gunnery skill if those militaries use biological, chemical or nuclear capable mortars or tac missiles. Precedent -- in WWII, the renowned US 4.2" mortar was originally deployed to deliver chemical munitions; it's called the 4.2" "chemical mortar". It was fielded in separate "chemical mortar battalions" that were, for all practical purposes, separate artillery units. One battalion was typically attached to a US infantry division. The mortars were very effective battlefield weapons, despite never firing chemical rounds.
Later on, the US deployed the "Davy Crockett", an unguided rocket launcher with a tactical nuclear warhead. The weapon was an otherwise unremarkable rocket launcher, but its nuclear warhead made it special and specialized units operated it. I think that they were artillerymen, but I cannot confirm them.
FA Gunnery skill apparently covers all the artillery systems on the Artillery Table, page 48.