An eligible unit is one that is within Engagement Range of an enemy unit and/or made a charge move in the same turn.
This is normal units for eligibility.
Units that made a charge move this turn fight first in the Fight phase. This means that units that did not make a charge move this turn cannot be selected to fight until after all units that did make a charge move have fought.
This is the rule that indicates that chargers fight first, which is equivalent to non-chargers cannot be selected to fight until all chargers have fought.
An ability which removes eligibility until X condition means that a unit is no longer eligible to fight until X condition is met. In most cases, this is after all other eligible units have fought. At that point, the unit that lost eligibility regains it.
If a unit is not eligible, it cannot be selected to fight. So a unit that charges, and then has its eligibility removed, does not fight first despite the rule that says a unit that charges fights first. It in fact, fights last.
A unit that charges, and then is made "not able to be selected to fight until after all other units have fought" or some similar wording, fights during normal sequencing as the Rare Rules section tells us these two rules effectively cancel each other out and we fight as if we have neither rule.
Does that clear things up for you?