I have the same question.
My best guess is that perhaps the gerund form is form specific ongoing action, and the infinitive form is for a general act.
Like maybe saying "Él siguió beber" means he continued [the habit of] drinking. Like maybe he's an alcoholic.
And maybe saying "Él siguió bebiendo" means he continued drinking [in that moment]. Like you asked him to put the beer down, and he continued drinking it (bottle to lips, head tipped back).
Any thoughts/confirmation from anyone on that?
I feel it should be accepted, but for me it is more usual to say 'He kept on drinking . . ." I don't know if the absence of 'on' would make a difference or not, and I am not sure it's actually more common than simply 'kept." It just may be my personal way of expression. Regardless of whether or not they accept it, you definitely have the right idea, and that's the most important thing.
It is in the dictionary. You just have to look in the right place. Are looking in the section regarding intransitive usage? This is right section of the dictionary where you should look.