Half-hearted, a.
1. Wanting in heart or spirit; ungenerous; unkind. B. Jonson.
2. Lacking zeal or courage; lukewarm. H. James.
Shades of meaning
Fernald has no entry of its own for half-hearted; he lists it under faint.
Where he writes about it:
A person may be faint when physically wearied, or when overcome with fear; he may be a faint adherent because naturally feeble or purposeless, or because half-hearted in the cause; he may be a faltering supporter because naturally irresolute or because faint-hearted and timid in view of perils that threaten, a listless worker, through want of mental energy and purpose. — from faint