The question as to whether a flooded battery needs to be equalized or not is easily answered, by using a hydrometer.
How often an EQ charge is required depends on many factors such as the average depth
of discharge, how often since the last true 100% recharge, how many partial recharges, temperature, battery age and health
An EQ charge should only be attempted after the battery has sat at ~14.8v until amps taper to about 2 to 3 per 100Ah of capacity, and then the voltage cranked up to 15.5 to 16v, with voltage sensitive appliances/devices removed
I found my one flooded group31 battery took 4 hours at 15.5v to max out SG on all cells but took only 45 minutes at 16v.
This 130 AH battery required 6.2 amps to achieve 16v after a few hours at 14.9v. I could do it on 200 watts of solar alone, if the battery was nearly fully charged in the morning, and the sunlight was uninterrupted. Usually amps had tapered to 4.2 to 4.4 at 16v when SG had maxed out at ~1.280, and later on I used my ammeter rather than the hydrometer to determine when to stop the EQ charge.
When one does not have the absorption voltage set high enough, and for too short a duration, then sulfation will form much quicker, Specific gravity will tank, and voltage under load will drop more drastically than a healthy battery.
The heavily cycled battery requires a different time at absorption voltage than the lightly cycled battery. There is no One size fits all formula as to how high, how long Absorption voltage is to be reached and held and no formula as to how often an EQ cycle needs to be performed.
The Hydrometer is the tool to allow an intelligent decision for these variables. Other people's 'Just Fine' stories as to what they believes works for them mean very little to somebody in a different climate, with different batteries, in different usage patterns.
Trojan lists a 14.8v Absorption voltage at 77f. Hold this voltage after each significant discharge until specific gravity returns to the 1.275+ level, compensated for battery temperature, and an EQ charge might never be required.
Allow only 14.4v and not enough time at 14.4 after a significant discharge, then the EQ charge will be required much more often, and be required to be held much longer before Specific gravity on all cells approaches their maximum baseline.
So as to how long or how often or how high a voltage is required in any specific usage, can only be definitively determined by the battery owner, armed with a hydrometer and the ability to achieve 15.5+ volts at the battery terminals and hold it as long as necessary until specific gravity no longer rises, or battery temperature starts rising rapidly, or is close to 120F already, or the amps required to maintain these EQ voltages begin to increase instead of tapering as usual.
My previous USbattery, group31, required, on a solar only recharge regimen, when depleted to 55% to 70% state of charge nightly, a 14.9 absorption voltage held for 2.5 hours, then a 15.3v finishing voltage held as long as the sun could hold it. By the 14th deep cycle, even with these rather absurd voltages and durations held after each discharge cycle, the Specific gravity had walked down to the 1.255 range, and I'm move all loads to the other battery, crank it upto 16v and 45 minutes to 2 hours at 16v would be required at 16v before 1.280 was attained again and performance restored to the maximum remaining capacity.
I got nearly 500 cycles from this battery, which is all that can really be expected in such usage of such a dual purpose 12v battery.
If I did not perform the 16v EQ cycle every 14 cycles or so, voltage under load performance dropped to hideous levels. If i waited to do an EQ charge every 30 cycles, the time required at 16v was doubled or tripled before SG maxed out and performance was restored.
Toward cycle 500, one cell, closest to the (-) refused to rise above 1.255 and it would heat up at the bottom of the cell about 20 degrees more than the rest of the battery. The Amps required to reach 16v were higher, and would barely taper as the SG on the cells approached 1.280. And of course water
usage increased significantly at the end of its useful lifespan.
The final hail mary EQ charge on it, the amps required to attain 16v was over 7 amps, and never tapered at all, and after about 25 minutes just started increasing. I took it out of service
I am not saying all flooded batteries require this same regimen, just that i spent a fair amount of effort experimenting to find the happy medium which allowed me to get my moneys worth out of this battery, and learned a heck of a lot in the process.
Flooded Battery care need not be mystifying, An Ammeter and a hydrometer are wonderful tools, as is an adjustable voltage charging
As far as bypassing the solar controller to achieve EQ voltages, I'd recommend waiting to do so only after amps at 14.8 have tapered to 2 to 3 per 100AH of battery capacity. Only then, allow higher voltages by directly connecting the 12v nominal panels directly to the battery, and of course disconnecting all loads which might be damaged by 15.5+ voltages, or loads big enough to not allow battery voltage to climb to 15.5v.
Dip the hydrometer every 15 to 30 minutes and stop the EQ charge when SG, compensated for rising electrolyte temperatures, attains 1.275+ on all cells, or amps required to maintain eq voltage begin to rise instead of taper or battery temperature begins to rapidly rise or approaches 120F.
If One cell's SG decides to stop rising when all the others are at 1.275 or higher, it might never respond no matter how long EQ voltages are held. If so then the clock just started ticking faster. I'd say to Expect no more than 50 to 75 more deep cycles from the battery before the capacity loss is so profound that even the most casual observer of voltage under load would know something is seriously amiss.