on the other hand healing Light HAS a ranged ATTACK icon
That was caught last week, it is not actually a light attack which is represented by a globe of light. The symbol you see there is a Hand with light emanating from the Palm which is the symbol for healing.
Looking at the card I would say that it is a Ranged Attack [0-1] so Hawkeye would spiff the cleric.
The Cleric's heal is not an attack.
There are two types of Bars
-Rulebook page 22 describes the Attack Bar
-Rulebook page 11 under "special actions" section describes Ability Bars.
Visually they are different in that Ability Bars are Gold-ish and Attack Bars are Silver. (that isn't mentioned in any text ive found, though. it would be a nice clarification to include whenever an update pass occurs again)
Now, sometimes an ability is an attack, but in those cases it will specify. For example, The Wizard's Arcane Zap is an ability bar, but in its description it specifies that it is a "quick attack spell".
The Cleric's heal is in an ability bar, and does not have a descriptor to suggest that it is an attack, so while its a ranged ability its not an attack and wouldnt get +1D (Nor does Hawkeye give +1 Die of damage to the Forcemaster's Pull ranged ability, handy as that would be.)
If it were an attack, not only would Hawkeye give it +1, but the other odd effects would occur:
Reverse Attack would sling the Heal back at the Cleric
You could roll a defense against a heal and dodge it
An interceptor could catch the heal instead of letting it go to the intended target
A Mage using Altar of Peace would have to pay 1 extra mana to use the heal ability
A similar example is Huugin's ability to peek at hidden enchantments, or a Wand of Healing's attempts to remove conditions/heal.