I've found that following the StrongFirst Fighter Pullup Program has worked wonders for me and others that I've recommended it to.
Although it's not a true greasing the groove program, you can use it as such. The rest between sets is the interesting thing here, if you're able to, then you're better off stretching the sets throughout the day so your body is fully recovered between them. If you don't have that capability, then I'd suggest a minimum of 10 minutes between sets to allow CNS and muscular recovery before the next set (making it more like a GtG program).
Since you currently max out at 2 reps, if you're able, I'd add a band into the mix to bring up your reps more to a rep max of 3 or 4 reps.
This program has you doing pull ups for 5 days, taking day 6 off, then starting again.
If you're going to stick with a GtG program that has you doing 50% of your rep max (so, 1 rep) for multiple sets throughout the day (I have a pull up bar on my stairs, so I knock out a couple of reps every time I walk into the kitchen), then you'll probably find that the ebb and flow of everyday life means you'll take a day off on occasion anyway. For me, when I go to visit my partner at the weekend, there's no pull up bar, so obviously I can't train pull ups GtG style.
If you've been training GtG style non-stop for a few weeks, then don't be afraid to take a few days off and see how you're progressing.