That's why this is another issue I see, but that others disagree with. To me, this is pretty clear in terms of the rules, but AFAIK there isn't a specific way to look at it. It has to do with the action economy. Let me start by making an analogy-
5e24 is specific about the action economy. For example, there is a difference between an "Attack Action" and a "Spell Attack." So if you take an attack action, you get the equip/unequip. If you take the spell attack, you don't. This normally doesn't matter, but if you use a "spell attack" that happens to involve a weapon (true strike) ... then it can matter a great deal. See what I mean?
What is a bonus action?
A Bonus Action is a special action that you can take on the same turn that you take an action. You can't take more than one Bonus Action on a turn, and you have a Bonus Action to take only if a rule explicitly says so. ... You choose when to take a Bonus Action during your turn unless the Bonus Action's timing is specific.
Actions-
... You can take only one action at a time.
Attack [Action]-
When you take the Attack action, you can make one attack roll with a weapon or an Unarmed Strike.
(Rules Glossary, and I confirmed it before typing- from Bonus Action, Attack Action, and Actions)
Let's move away from handcrossbows to a Scimitar (light, nick) and Shortsword (light, vex).
Assume level one, equipped with both, nothing else going on.
Krom takes the attack action. Since he is using a light weapon, he can take a bonus attack with a light weapon. But bonus actions require a specified trigger. So which weapon is the attack with the light weapon, and which weapon is the bonus attack occurring with? Krom has two choices:
A. Attack with Scimitar (nick), bonus attack with shortsword (vex).
B. Attack with Shortsword (vex), bonus attack with scimitar (nick).
Now, Nick-
When you make the extra attack* of the Light property, you can make it as part of the Attack action instead of as a Bonus Action. You can make this extra attack only once per turn.
So in A, he is making the Attack Action with a weapon that has Nick, so when Krom "make{s} the extra attack of the Light property, {Krom} can make is as part of the Attack action instead of as a Bonus Action."
But for B? The Attack Action doesn't have nick. The Bonus Action was triggered by the light property, and it is still a bonus action. The extra attack was not triggered by the nick weapon... but by the second weapon being light, so what happens is that you end up with just the attack action and the bonus action, but you can't retcon the bonus action back into the attack action.
Notice that for 95% of use cases it doesn't matter; just remember that the "first attack" is with the nick weapon. But it does matter in terms of restricting a few cases.
Anyway, that is how I read it.