If you have a 180A multimeter, yes. But I suspect not. (Most are 10A & you'll blow the DMM fuse.)
I still reckon disconnect the BattCap for now. I doubt that it is doing much good - or rather, it probably won't be helping the lights NOT dimming. (Connect it back later. If fully charged, it should last a year or 2 without charging, but just in case...)
And ok - crank as in volume. (Remind me to abuse you later.)
In that case it is wiring or the alternator not keeping up.
A voltmeter is the ultimate test.
But to check you amp currents (in Amps, not in head units), either a shunt else an appropriate sensor.
Current shunts may be $2o or more. I use a $10 50A shunt to measure starter motors (from ~140A to 250A or more) and 50A is adequate for short term use. Generally I'll only cranking (the starter!) for a minute or less - not enough time for the shunt to heat up. (The 50A rating is long term; it is overheating that will destroy it.)
I've been meaning to buy a few 200A or 600A DC sensors for about $20-$25 each (USA - DigiKey, DC Hall Effect sensors - loop type, 5V supply etc) for monitoring and zero-resistance protection for hi-current car systems (like winches & audio - you'd think the latter would use zero-resistance fuses wouldn't you?).
Both work similar - eg, a 200A shunt or sensor might be 1mV/A (or 1 milli-Ohm for a resistive shunt) which means 1mV per Amp. So 200A = 200mV. You set your DMM to the 200mV or 2V DC scale and read off the current.
Note that for non-resistor type sensors (eg, Hall & loop sensors), it is important to specify it's for DC - most are for AC.
Or there is always approximation from the cabling or fuses. If their resistance is known (eg, if 0G is 0.0983 Ohms per 1,000' and you have a 5' run, that's 0.0983/1000 x 5 = 5x0.0983 micro-Ohm = 0.4915 uR (u=Ohm) or 0.4915 uV per Amp - ie, 49.15 mV or ~50mV per 100A (from V=IR).
In fact many "remote" ammeters work that way - a voltmeter or DMM is placed across the ends of a ground strap or battery cable and calibrated to read in Amps.
If you load exceeds the alternator output (at a particular RPM etc), then the alternator voltage will drop from (say) its max of 14.4V (or 14.2V whatever) to the battery voltage.
The battery voltage can be anything from ~13.8V if it still has surface charge (after being at 13.8-14.4V), then drop to ~12.7V (a battery full voltage) and the drop lower firstly due to internal resistance (ie, a fully charged Optima yellow may have 0.003 Ohms internal resistance; if it discharges at 100A, that means V=IR = 100 x 0.003 = 0.3V drop hence, (say) 12.7-0.3 = 12.4V at its terminals, not 12.7).
So if the alternator is under supplying by 100A, instead of a 13.8V to 14.4V
system voltage, it drops to 12.4V (nearly 2V less which means almost a 40% power drop for traditional lights etc); and a 1.5-2V voltage drop has a big effect on halogen lights (more than for tungsten etc; but HIDs should not be effected).
As the battery discharges, not only does its (open circuit aka internal) voltage decrease, but its internal resistance increases thereby leading to a spiralling doom for audio systems (maybe clipping etc).
So in this short reply, you may see some of the issues.
You see the effect of a 0.003 Ohm battery resistance. Add to that the cabling resistances, fuses, distribution blocks, and every connection that adds a small bit of resistance..... that includes ground paths.
You may also see why a low ESR battery can be severely compromised if far away from the load/amp. (ESR = Effective Series Resistance. It is close enough to the battery's internal resistance. And a battery's ESR is quoted for a fully charged (and new) battery (usually at room temperature).
So, figure out if the alternator is under supplying.
Then figure out if distribution resistances can be decreased further.
And by placing the yellow top at the amp you can concentrate your real heavy wiring there (shorter hence cheaper runs of bluddy expensive cable).
A
normal battery can be used for the rest of the vehicle. (Typical ESRs being ~0.015 Ohm or less. And as I recall, the rule of thumb being that an AGM battery has about half the ESR of an equivalent capacity flooded (wet) lead-acid battery.)
Now, there was something I was going to complain about.....?
... No, it's not about DY sneeking in with a 5-word reply that has a huge probability of negating all I said above (ito usefulness for OP's solution; it still serves as a ref for my future scribblings....)