Hello @Jjhill and welco.e to the community.
Are you still in grade 1 with 2 chord songs?
As you count try to do so melodically and in that way you can shape the melodic nature of your counting to approximate the vocal melody. It will not come immediately and you will have to spend conscious effort on it. Eventually you may find you naturally incorporate some fragments of lyrics in with the counting and eventually replace the counting with more and more lyrics until you can do the whole vocal.
For playing aling to a track and counting check this topic.