It was arguably a recurring feature since the proclamation of Eudes as king in 888, including the proclamation of Robert and Raoul , with Aquitain potentes being generally unsupportive of Robertian claims (while not being systematically supporting Carolingians as well) as it was seen as a threat to their own northern influence/territories.
But the war of succession of Aquitaine/Auvergne between Ramnulfids and Raimondins did changed things, and allowed some Robertian networking in the region (including matrimonial union with Ramnulfids). Thing is Robertian hegemony in Francia proper quickly declined in the late Xth century, and other families had vested interests in Aquitaine as well (Ingelgerians, Plantagenêts, and Thibaldids, notably).
So, initially, Guilhèm IV went with the general situation in WFrance, probably having a similar policy than his brothet-in-law, Eudes of Blois : supporting a Robertian king that wouldn't be too powerful, but enough to prevent another house issued from Robertian decline to meddle too much in Aquitaine
(We don't have much about Toulouse in this period, to the point that several counts might have been overlooked in the official list : it seems they didn't have much interest on what happens in the North, everything goes as long they're not involved, which paradoxically helps Capetian claims)
The duke changed his mind with Hughes Capet breaking his word and constraining Charles, which happened in the same time that Hugues wanted to enforce his claims on Aquitaine. But it was relatively resolved quickly, because nobody really had an interest (or the possibility?) going full war.
The main issues seems to have come later, in the last decade of the century, when you had a very general aristocratic opposition to Hugues, and even there Guilhèm's hostility seems to have been relatively lukewarm. By the time Guilhèm IV acknowledges Louis as a possible king and host him in Aquitaine, the opportunity to set up Louis on the WFRench throne is gone, Robertians having rooted their presence and Ramnulfids having few allies left in Northern France that would consider overthrowing Robert II. This isolation (and the relative couldn't care less attitude of southern potentes) prevents at this point a real chance of a separate Aquitain kingship : in fact, even the idea of an integrated kingship seems to be gone at this point, due to the general disorder.
So while Guilhèm IV does seems to have supported the idea of a Carolingian king past 987, it was relative to its own interests and the more serious attempts were in alliance with French potentes. I think it's relatively too late, safe some changes.
- Either reduce or butterfly away the War of Succession of Auvergne, in order to make Aquitain territories at least roughly unified
- Have Late Carolingians effectively having a hold on Aquitaine, even if it's likely it would be essentially trough networking. If not the whole concept of a distinct Aquitain kingship from French kingship wouldn't even be considered, and at best it would mean a step ground for taking back French kingship as it happened IOTL in the Xth century.
- Have Charles of Lower Lotharingia being crowned king in 993, delaying the succession crisis in a XIth century where Robertians would have an harder time being considered an alternative. Maybe, but that's open to discussion, Ottonian influence (which was a really important factor in Xth century France) to prevent a French takeover of Lotharingia (that Charles would probably have been forced to give to his son definitively, but that wouldn't at the latest provide certainty that the duke wouldn't join French armies), which was the usual obsession of Late Carolingians, and act in favor of a divided kingship in France and Aquitaine, with the clear idea influencing both, or at least Aquitaine.
(I may have missed several things, the whole situation is clear as mud, so i'll check on what I have later)