Good advice from bluesmadd.
I will add some food for thought.
Caveats:
I think it is hard to separate counting from other aspects of playing - everything has to work together and counting is just one aspect of playing.
This is what works for me, may not work for you as we all learn differently.
This is my opinion which may or may not be correct or agree with the opinions of others.
A lot of this depends on where an individual is in their learning process, and their achieved level of technique.
First, it's not clear exactly where you are experiencing trouble counting - is it on the licks themselves, or in general, everywhere?
In my opinion, as you progress through SBS and the solos become more and more difficult, you will NOT be counting many of the licks. I just don't think that it's possible to count many of them. I mean really, how do you count 35 notes in one measure at that speed. Forget it - its'not going to happen.
In fact, I rarely count licks at all except maybe when initially learning a lick as I "sight read" it for the first few times to try to hear what the lick sounds like and get the note sequence in my head.
I recommend initially learning the licks as played - with Griff's material, we are so fortunate to have both an example of the actual playing along with the notation and tab. Playing along with Griff (almost always slowed down) to get a solid grasp of the "feel" of the lick is essential to me.
What is the big benefit of this? Two things - 1) your playing will sound like much more "authentic" blues, because there are often nuances in the playing that are not reflected in the notation or tab that make it really sound like the blues. 2) Once you can play the licks in this manner, you don't NEED to count them.
So, once you have the licks well in hand, it's time to string them together, and HERE is where counting is MOST important IMO.
For it to sound right, you need to start and stop and restart playing at the right times. This means that I really only count the rests, and sometimes the duration of "held" notes (longer duration notes). This may take some time to work out, and it helps to carefully listen for specific "cues" in the backing track to key off of for places to start counting from. Identify your problem spots via a self recording along with the backing track. Then practice this, counting along with Griff's playing at first, then hum the licks or play them in your head along with the backing track and practice the counts, and then add actually playing the guitar yourself and counting.
This is a big mental task that most of us cannot conquer in one fell swoop (unless your name is W. A. Mozart). This process breaks it down into several sequential steps that build on one another after the previous step can be accomplished with little or no conscious thought, which allows the brain to more efficiently and successfully multi-task all of the things that go into playing.
Note: Using backing track cues is good only if you always play along with that backing track. Eventually, you should move beyond that as it all becomes more second nature, and rely on your own playing and counting - in a jam situation, you won't have the same backing track cues to work from. It's a process that takes time and complete familiarity with the piece.
So, in summary, my process is to learn to play the licks by "feel" and count the rests.
I hope maybe some of this makes sense and might help.
I am still, and will always be, working on mastering this process, this approach has helped me.
Tom