Okay. Let's assume for a moment that Spekkio is who he says he is, God of War. Gods in Roman mythology went along with the flow of time just like any normal person, so Spekkio has been around all through the ages and whatnot. Time eventually comes to an end, but since Spekkio is immortal-God-guy, he's left to his own devices at the EoT.
Now for the pillars of light. They link to many important time periods of that planet's history. I assume that can't be random; they so conveniently linked to every time needed by Crono and Co. to rid the planet of Lavos, so I think it's a good chance that the Entity put them there. In all possibility, after time ended, the Entity probably put Spekkio there for the same purpose as the pillars. So if Spekkio is the God of War, and the creation of the Entity, then he's like some sort of Son-of-God type deal, except warlike. And it could be said that he holds the keys to salvation from Lavos, since he unlocks the magical ability of Crono and Co., since without it they wouldn't get very far against Lavos.
ok, understandable enough. however let me offer my viewpoints based on a few details gathered so far that are not pure speculation:
(1) Spekkio refers to himself as the Master of War and says he watches battles from his vantage point.
(2) In the Japanese version, he refers to himself as the "God of War", so he is a god of some sort.
(3) He alternates forms/battle tactics based on the strength of his opponents.
(4) His strongest form seen is a red Nu with all of the strongest spells the characters possess combined, and others not used by the party.
(5) He can use multiple elements with ease, many spells that are apparently not shared with other characters can all be found with Spekkio.
Speculation begins:
(1,2) Spekkio is a "god", created by Gaspar for reasons unknown.
(1,2) Spekkio is a "god", created by the Entity for the purpose of equipting Crono and company with the tools they need to defeat Lavos.
(1,2) Spekkio is a "god", how he came into existence and the reason for his presence are unknown, but he has survived beyond Time's ending and now lives with Gaspar, who was sent to the End of Time via a gate Lavos created.
(1,2) Spekkio is actually a Nu and is bound by whatever laws the Nu exist by, which were discussed my earlier in this topic, but I'm not going to bother listing them out

(3) He can shapeshift, implying no permanent form, he offers to fight the party for practice, and regardless of the victor, everyone comes out unscathed.
(3) Going from what I said above, he has the ability to instantly heal the party or:
(3) Going from what I said above, his attacks aren't "real"; they don't actually do damage, the party just assumes it during the fight, as if "mind over matter" thoughts took over during the fight. One could make this connection to the thought that he is a product of Gaspar, specifically, Gaspar's dreams.
(4) If he does not possess these spells, perhaps he can mimic his opponents understanding of magic, giving him a powerful edge to always have his enemy's best move within his grasp.
(5) He is truly a god, he is all-powerful. or:
(5) He is Shadow-based, but very skilled, so he can use all of the elements just as Magus can [he can sense Magus's power when they meet, he says that Magus could teach him a thing or two. or:
(5) He is a god, he isnt based on any element, he has a perfect balance of all four so he is free to do as much as he wishes with them.
So yea, I think I've covered many of the important details about Spekkio so far, add as you wish of course.