Bea's tail pocket is like you're describing....very deep. I can get the whole tip of my forefinger in there to wipe it out. I use the same thing DesertSkyBulldogs uses - those MalOKet wipes. Got mine at Amazon.com. It's really a daily activity for her and since we've been doing it since she was a wee pup, she holds still for the activity. (In the beginning, she got a treat every time for this. )
Bo has an "outtie" so his cleaning is limited to the "crease" between where the tail meets his bum. My EB Mable used to get sore/itchy there from time to time as evidenced by the "break dancing", I call it. (when there's nothing that needs to be expressed in there - obviously)
Bea was break dancing yesterday evening and it occurred to me that I hadn't been in there to clean in some days - four to be exact! Wow. It was a mess. I wiped until the cloth was clean after the last swipe thru there..... Won't be forgetting that again!