Does a player have to declare a target in the trash before Heedless Resurrection resolves?

Yes, you must declare the target in your trash at the time you play Heedless Resurrection and place it on the chain.

According to RiftJudge FAQ #9523 and Rule 355.10.a, when playing a spell that targets a card in a public zone (such as your trash), you must declare that target during the finalization process—before the spell is actually played and before your opponent has the opportunity to react.

The sequence works as follows:

1. Declare/Finalize: You announce you are playing Heedless Resurrection. You select a unit card currently in your trash as the target.
2. Lock-in: Targets are locked in at this stage (Rule 355.15). You cannot change this target later, nor can you wait to see if your opponent reacts before choosing it.
3. Cost: You pay the additional cost (killing a friendly unit) to finalize the spell to the chain.
4. Chain/Reaction: The spell is now on the chain, and your opponent has the opportunity to play Reactions.
5. Resolution: Heedless Resurrection resolves. Because the target was already chosen and locked in during Step 1, it must be the same unit you initially declared.

Because the unit you intend to kill to pay the cost must be on the board (and not in the trash) at the time you initiate the spell, and targets must be declared before paying costs, you cannot kill a unit and then immediately target that same unit in the trash with the same Heedless Resurrection.