A forward non-trigger literal is like a forward trigger literal except that what is isolated from the antecedent of a forward rule is the literal (or literals) that, though true, will not trigger the forward propagation of the rule. I.e., when a literal is asserted, if it is a forward non-trigger literal of a rule, then that rule will not fire. This can also cause race conditions; if the non-trigger literal is asserted last, the rule will not fire.
It should be noted that placing a forward trigger literal on a rule effectively makes all other literals of the antecedent non-trigger literals.
For more information, see the training module Logical Warrant vs. Pragmas.