My earlier taxonomy effectively identifies subjective reason with free motivation - though I should be careful not to confuse recognition of a fact that is a reason with recognizing that fact as a reason. Of course we will be motivated by whatever we see as reasons, i.e. what I taxonomized as "s-reasons". But - the more important question - what about "p-reasons"? Are they possible? Might we recognize that some fact (which just so happens to be a reason) is true, yet fail to see the fact as a reason? This is not so clear.
Suppose not. Then we might seem to be committed to a desire-based theory of reasons:
the core assumption... is that a reason is necessarily something that would guide the action of an informed agent. But according to the belief-desire theory of action, all action aims at desire-fulfillment. So the agent would treat as action-guiding only information that was relevant to the fulfillment of his desires. If you presented him with a 'reason' which appealed to some end that he did not share (i.e. desire), then he would not consider it a reason to act at all.
But is this 'potential motivational force' truly essential to the concept of a reason? Must an objective reason be recognized as a reason by all factually-informed agents? If so, then it would seem the amoralist is correct. From the mere fact that the (informed) amoralist is not motivated to act morally, it would follow that the amoralist has no reason to be moral. But we might wish to deny this, and hold that the amoralist is in error: there are reasons for action that they are failing to recognize, namely, those provided by the demands of morality.
Let 'rational internalism' (not to be confused with moral reasons internalism) be the claim that reasons must potentially motivate, as above. (That is, the denial that p-reasons are possible.) Does rational internalism vindicate the amoralist? I think there are two ways this could be avoided. One would be to deny belief-desire psychology, and argue that there are intrinsically motivating beliefs ('besires'). That sounds odd to me, but some philosophers do defend this view. (I wonder what psychologists have to say about it?) The other option is to claim that new beliefs could influence our basic desires, which again I find implausible, but as it's a psychological question, we philosophers probably aren't in any position to comment.
Leaving aside those complications then, we have the two basic options: adopt rational internalism and admit that the amoralist has no reason to be good, or else reject rational internalism. Which option do we have most reason to pick? [And how would the rational internalist answer if I had no motivation to adopt his theory? ;)]