That pulsing means your battery is "full", so what you have is working well enough to keep your battery full and that's probably good enough, nothing fancier required unless you need something more from the system. (i.e. more power, faster charges.)
Actually it does not always mean it is "full" it only means it has reached absorption voltage or the OFF voltage of the controller. This can happen anywhere between 80% and 85% SOC on most banks. Flex Charge shows this in the graph above. The first black line is getting the battery to 80%. The controller then shuts off and the batteries have to fall to 13.6V for it to turn back on.
Below is a video of a Flex Charge PV-7. It shuts OFF at about 14.4v and does not come back on until the bank voltage has dropped to about 13.6V. This video is showing the "current" and you can see it turn on and off. I applied a load of 0.1A just so it would go to -0.1A when OFF for the video. Once in absorption voltage range your OFF time can be as much as 10-20+ times longer than your ON time with some cheap controllers.
This is a video made sing the same Flex-Charge but showing the voltage ON/OFF points.
In this case the "ON" time is about 5-6 seconds and the OFF time close to a minute to get the bank back down to 13.6v before it can turn back on again. This bank still had 20 Ah's to go, a long way from full, and it would take 5-7+ days for this bank to eventually get "full" from an 80-85% state of charge with 5-6 seconds on and 60 seconds off, remove the 0.1A load and it would likely make this even longer.. When you figure on about 4-4.5 hours per day of good sun, where your panels can produce, and you are on for 5-6 seconds and off for 60 seconds how much time is actually spent charging once you hit 80% SOC.....? Not much....
It should be noted that before I took the video the bank was charged to full using a shore charger until they were accepting less than .5% of C (capacity) at 13.6 volts. At this point, after being on float for two days, the battery monitor was re-calibrated manually to full. I then applied loads and removed approx 30 Ah's from the bank. I then monitored the time it took to replace the 30Ah's removed.
Contrast that Flex Charge controller, or a Sunforce, with a quality PWM like a Morningstar or MPPT like the Genasun's and the difference in the last 15% of charge, and the time it takes, can be quite dramatic.
I used to have a Flex-Charge on my own boat and have a couple in the shop I can use for experiments like this. Do they "work"? Of course, but the last 10-15% takes a lot longer with an ON/OFF controller than it does with a PWM or MPPT. Getting batteries back to 100% as quickly as possible leads to longer life and less sulfation.
On boats we usually have no loads when we are not on the boat because the batt switch is off. This causes the controller to easily get into the ON/OFF voltage behavior once the batts have reached absorption range or 80-85%. Even a small load, like in many off grid installations, makes the voltage fall faster so it turns back on faster. The Flex-Charge is a better shunter because the off is 14.4 and on around 13.6. Some of the Sunforce shunters don't turn back on until 13.0V. I once watched a bank of AGM batteries, Oddyssey, hold over 13.0V for 70+ minutes before the Sunforce controller came back on.
Last summer I replaced both a Sunforce and a Flex Charge shunting controller with small Genasun MPPT controllers. On one boat "FULL" was cut from averaging 7-8 days, if at all between sails, to about 2 days and on the other boat "FULL" was cut from roughly 5-6 days, if at all between sails, to about 1.5 days. Same boat, panels, wiring, batteries, just a better quality controller that does not turn ON/OFF like a shunter will. A lot of the controllers you buy from "discount" solar houses & eBay sellers are "shunters".
I have replaced a number of eBay, "so called", MPPT controllers that were not MPPT at all so be careful what you buy. They were complete scams. The harsh reality is that behind the "MPPT" sticker and box was nothing more than a simple shunting ON/OFF controller. MPPT & PWM controllers do not shut off for long periods of time like shunters do. The average Joe does not know how they should work so these eBay scammers often get away with it.
The small Genasun MPPT's are a very good value for smaller for panels. When I have a larger array I generally use Blue Sky or Morningstar MPPT controllers though I still use some Morningstar PWM controllers too. The off periods on MPPT and PWM are very, very short in duration and often not even visible on a monitor.
The Flex Charge controllers do "work" but time to 100% SOC is slower.. In bulk same as a PWM but the last 15-20%, above 80-85% SOC, not much comparison...