Yes, Kronk should be allowed to wait for Brand. The answer needs a careful reading of multiple sections of PHB as well as the DMG, as AD&D was much more a guideline, and less a rulebook as compared to later editions.
Before we begin, it is best to understand what the 2e designers had in mind regarding initiatives. From your question, we infer that you are not using the default group-initiative option outlined in the Player's Handbook. If you were doing so, the player characters could/would act together. But even if the individual initiatives are being used, we will read below that the rules explicitly encourage the DM to take responsibility and allow players to do the sort of thing you are asking. Anyway, the following quotation by Steven Winter is useful to put us in the right frame of mind regarding initiatives (emphasis added):
This topic was hotly contested while we were working on 2E. I played a lot of Melee/Wizard and was a big fan of its rigid definitions for what a character could do and how far he could move under various circumstances. Zeb favored the exact opposite view, that the less these things were defined, the more the DM and players could bring the scene to life and adapt to anything. We debated that more and longer than anything else. The standard rule is Zeb’s; the individual initiative rule is mine. In the end, however, I came over to Zeb’s way of thinking. For a game like AD&D, I now prefer the standard rule with its heavy dependence on narrative and interpretation. Which is not to say that I dislike or disavow the individual initiative approach. It serves very well for one, entirely valid style of play. I’ve simply come to appreciate a different style of play more.
According to "The Combat Sequence" section of the revised AD&D 2e Dungeon Master's Guide (as well as the Player's Handbook), within a combat round a fixed set of four steps are followed:
- The DM decides what actions are to be taken by the monsters and NPCs.
- Players decide what their characters are going to do.
- Initiative is determined.
- Declared actions occur according to the order of initiative.
Note that first the declarations are made and then the initiative is determined and we finally get the resolution, so it is usually not possible to change your course of action according to what is going on.
However, a couple of paragraphs after this description, we read the following (which also reflects the mindset described by Steve Winter in the preamble; emphasis added):
The above sequence is not immutable. Indeed, some monsters violate the standard sequence, and some situations demand the application of common sense. In these cases the DM's word is final.
How do we "calibrate" common sense for the resolution of this question? There are two explicit rules that we can read for this, one in the actual description of the initiative (page 93 of the original Player's Handbook), the other regarding "waiting" for other parties to act (in the section "Encounter Options" on page 112):
The initiative roll determines who acts first in any given combat round. Initiative is not set, but changes from round to round (combat being an uncertain thing, at best). A character never knows for certain if he will get to act before another.
Wait: Sometimes when you encounter another group, you don't know what you should do. You don't want to attack them in case they are friendly, but you don't want to say anything to provoke them. What you can do is wait and see how they react. Waiting is a perfectly sensible option. However, there is the risk that in waiting, you lose the advantage should the other side suddenly decide to attack. Waiting for a reaction so that you can decide what to do causes a +1 penalty to the first initiative roll for your group, if the other side attacks.
The first rule bars a particular character from acting before others. It does not bar them from intentionally acting after. One could counter-argue that "barring after" is also implied through atomicity of combat rounds, allowing no reactions at all, but the second rule seems to undermine such a strong interpretation, as it gives the PCs an option to watch and react to what an unfamiliar (and possibly hostile) party could do (at the cost of a minor initiative penalty).
How to do it
Now that we argued it should be possible, how do we implement it with a good narrative? It is up to the individual DM to handle the situation. One might decide to give a large positive situational modifier to the initiative roll of Kronk increasing the chances of him acting after Brand. Another might allow Kronk to wait until Brand's initiative if Kronk can roll above a certain number in d10, adjusted by his dexterity reaction adjustment (something like a dexterity check in the 3e parlance).
What our gaming group would do is to let Kronk's action happen at the very end of the round, ie. after all the other actions are completed (not allowing him to time perfectly). Here is one possible gameplay:
- The DM declares that the troll tries to grab Brand.
- Brand declares that he tries to cross the bridge. Kronk declares that he pulls the lever after Brand passes the bridge. Note that very quick feedback that can effect declarations of the actions, like Kronk's shouting, is ok between the players.
- Initiatives are rolled.
- If Kronk's initiative turns out to be higher than Brand, no problem, Brand runs, Kronk pulls the trigger. If, on the other hand, Kronk's initiative turns out to be lower, the DM rules that he is unable to time actions perfectly, so has to wait until the end of the round to pull the lever, which might mean that the troll has also passed the bridge to grab Brand, or the troll tried to grab and failed and Brand passed the bridge leaving the troll on the other side.
Appendix: Answer according to Player's Option: Combat and Tactics
The answer according to the combat system introduced in the Player's Option: Combat and Tactics sourcebook is straightforward, Kronk can definitely wait for Brand. Quoting from page 23 under the section "Choosing an Action":
..., a character can choose to either hold or abort a combat action when his action phase arises. Holding an action simply involves delaying the intended action for one or more action phases.
Even if you do not use PO:C&T, it is informative to see that its specific codification is in the same "common sense" as we described in the earlier sections of this post.