How old are you? Or with more pertinence (and impertinence), do you have any sacral degeneration going on at your advanced age?
A couple things happen as we get decrepit ... excuse me, old ... excuse me again, mature ... in the lower back. One is that the sacrum starts to deteriorate, and for many of us the lower lumbar vertebrae as well. The sacrum never had much mobility to begin with, but you have a lot of muscles attached to it to support the pelvis, the femurs, the spine, you name it. It can be the epicenter of all kinds of obnoxious problems and the sorry truth is that in our decrepitude we aren't going to be able to do too much to the sacrum itself. As it weakens or gets sore, your hip muscles tend to want to go passive in response to sacral pain, so you have non-firing hip muscles or very weak ones. Then your hip adductors go, then some of your lower back muscles, and then it all basically goes to hell. The answer is to reverse that whole chain of deactivations. Cycling won't do much because it is part of what caused it (that plus sitting, plus other behaviors our hips and lower back really don't like and were never made for). There are some people who are into using bands to reactivate muscles, others who use pilates and all kinds of other methods, but I tend to be a bit more direct.
Get the hips going, first of all. They are by far the most powerful and nothing works right until they do. Dead lifts are great for that -- you don't need to be Arnold, just have good form and lift enough to make your glutes work. This is not like the muscles have no strength; it's that they were conditioned not to work to avoid pain nearby. Dead lifts don't mess with your sacral pain too much; just don't go too heavy. Plus, you get almost immediate results -- you should feel better within a week or so.
Next, go after the lower back and the internal stabilizer muscles. The approach I find that works well for many people is a Glute Ham machine. Do NOT hyperextend with it; that's not the point and it can hurt you. Just use it to do like a reverse sit-up. Depending on how it's adjusted and which machine it is (leverage is very different among different brands), you'll also get very fast response from it. For cyclists you can find it's one of the best ways to improve your cycling and reduce any pain anywhere below the neck.
Then start pushing all the peripheral muscles. If you can find a speed skater's slide board (or make one -- it's very easy and cheap), it's a great natural way to build ab- and adductors. Much better and much more fun than bands. Start doing some short plyo jumps -- just 12 inches or so, but very fast and without crouching at the top so you really jump a full twelve inches. Even the height of a flight of steps will do -- just jump the stairs two-legged.
By now your pain should have eased and you should be feeling pretty good about your riding and sounding insufferable as you explain to all your riding companions how they could reduce their own blighted pains. When you really want to be banned from your team ride, start doing pistol squats (squats on one leg only with the other leg pointing straight in front of you until your hip touches your heel). Those take more power than most power lifts, but the best thing is that they teach you coordination. And coordination is one of the hidden issues here -- your problem really started, with a certain reasonable probability, when you stopped making each side of your body cope for itself and let your butt sitting on a chair or on a saddle cause your sense of balance and coordination to go to hell. Then everything else went wrong. You can't do pistol squats until you have the muscles working again, but once you can do a pistol squat (even cheating by holding onto the back of a chair for balance) you are fixing the fundamental origin of your sacral pain, lower back pain, tight hamstrings, weak glutes, tight ITB, and the plethora of other things wrong with you.