The problem is, that if we assume a going into synchrony and sharing fate means they interlocked and didn't leave again. Obviously, being both Carpatho-Balkan lineages, for the most part, they shared specific events. Like the Scythian and La Tene Celtic invasions affected them both negatively at first, you see the dents, but they reacted differently afterwards. Like E-V13 had one of its biggest expansions with Scythianised groups, after the Scythian invasion. J-L283 shows absolutely no sign of this. Even more important, some of the modern Albanian E-V13 subclades likely participated in this Scythianised expansions.
With the Celtic dent its different, both go down and up, but E-V13 double time of J-L283. Here you could argue they share the same fate, and its true, but this was affecting all of the Carpatho-Balkans, almost, so it doesn't tell us how closely they were, exactly.
My main concern is the Roman conquest period:
E-V13 had its darkest hours (about 0-200 AD in particular), going down to nothing, no new founder lineages at all in this period. At the same time, J-L283 stays stable and keeps growing.
That's a major out of synchrony moment, which needs to be explained.
When E-V13 goes up again, one could argue it looks like they closed the gap, but in fact, these later E-V13 upturns can be brought into synchrony with Germanic and Slavic migration and growth events as well. You see the solid uptick of E-V13 in the Slavic expansion period: That's 100 % in synchrony with the Southern-Eastern Slavic expansion of R1a and I2a. J-L283 goes down right there, but probably the Balkan E-V13 lineages did also, especially those in the early Albanians, that needs to be checked.
But what really bothers me the most is this Roman era complete out of sync moment for E-V13 and J-L283. E-V13 was more than double time as big as J-L283, and it goes down to zero growth, zero, nothing, after Roman conquest. That's so huge, its the single most important negative impact E-V13 ever experienced and its right in the time of the Roman conquest.
Its very tempting to associate that with the catastrophic defeats, wars, famines, uprisings and demographic downward trends assocated with the Roman era in the Celtic, Sarmatian, Dacian and Thracian regions. Very tempting to do so. For that time there is zero correlation between E-V13 and J-L283, so they had completely different trajectories. Completely different.
Even if going for the Albanian subclades, we already see that it must have affected them too, because E-V13 had zero growth in that time, zero!
For such a major lineage of Europe, which grew so consistently, even during times of wars and tumult, since the Early Bronze Age, never going down that much, you just can't overestimate these numbers. If you read up what happened especially to the Dacians/Daco-Celtic people in that time period, being attacked from all sides, like the Roman conquest of Dacia and the Germanic attacks on the Free Dacians, its very, very tempting to associate it that way.
And the recovery period of E-V13 was mostly carried on by tribals, not by Roman territories. You can see the first significant uptick being completely Slavic related and going against J-L283, which did not signficantly grow with Slavs. You see the dent, right about 600 AD for J-L283, while E-V13 goes steeply up, completely in sync with R1a and I2a Slavic clades.
So in the Roman period the two major Albanian haplogroups are diametral to each other, same for the Slavic expansion phase, but less pronounced. There are not small issues or events, these are no small numbers which could be explained by "chance".
It simply looks also like J-L283 was conquered by the Romans significantly earlier, like 1-2 centuries earlier. This affected E-V13 as well, negatively. But the J-L283 did fairly well after that, recovered and were growing, whereas E-V13 was cut yet again, like "the second half" of the growth it had before, and this likely shows the Dacian, Daco-Celtic conquest and Germanic invasion of Eastern Europe.
The Illyrians were defeated and largely integrated by 200 BC, finally about 160 BC:
https://en.wikipedia.org/wiki/Illyrian_Wars
The Dacian wars were 200-300 years later:
https://en.wikipedia.org/wiki/Trajan's_Dacian_Wars
That's exactly when J-L283 goes down first - and E-V13 too, somewhat, but then the biggest blow for E-V13 is right in the era of the Dacian wars. Hardly a coincidence, it just fits so nicely.