Has anyone tried this combination before? Eldritch Archer's abilities don't exclude firearms, so I think there's some synergy here. Not sure how to spread out the levels (I don't need more than 5 levels of gunslinger, because no one does. It's entirely possible that one level might be enough.)
Sure; touch attacks to use with ranged spellstrike are an obvious lure. It's feat-stretched between archery and a little metamagic but it works well enough.
One level of gunslinger then eldritch archer to 4 so you get 2nd level spells is a decent start. You can reconsider how to go from there.
I like Gunslinger, but even I'll admit the over-5 levels of it have become even less essential for gun-usage in the face of Martial Focus + Impressive Grit. IG will let you have a number of uses per day of dead shot, startling shot, or targeting equal to your Int-modifier.
Gunslinger is mostly to save on feats for the Eldritch Archer. You could also use Spellslinger instead, which will cost you some BAB but give you a good option that stacks with the usual arcane pool bonus.
Personally, I think if you're going for 5 levels of Gunslinger on a caster build, go for Spellslinger into Eldritch Knight so your casting catches up faster. You lose out on some action economy, but you really need that casting power more.
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Gunslinger is mostly to save on feats for the Eldritch Archer.
Yes. At low levels, this is good. At mid-levels, you don't need that since the Magus gets bonus feats.
You lose out on some action economy, but you really need that casting power more.
That's why you shouldn't go five levels of GS :) At any level below seventeen, the EA is going to have more casting power than a GS/SpS/EK (e.g. at level 13 the EA has fifth-level spells and the EK only gets fourth). Frankly this EK would benefit more from the action economy of spell combat, since he's not likely to catch up on casting power before the campaign ends.
That's why you shouldn't go five levels of GS :) At any level below seventeen, the EA is going to have more casting power than a GS/SpS/EK (e.g. at level 13 the EA has fifth-level spells and the EK only gets fourth). Frankly this EK would benefit more from the action economy of spell combat, since he's not likely to catch up on casting power before the campaign ends.
Prestigious Spellcaster is a thing now, so the GS/SpS/EK pulls even with pure EA at the 14th level. I'd agree it's still late, but you are getting a significantly better baseline damage output and spell list out of this. It's certainly not a build you would go for if spellcasting power is your primary concern.
This sort of build starts to shine if you have access to the Trench Fighter, since you've already caught up with single-class Magus by the time you're qualifying for Eldritch Knight.
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Prestigious Spellcaster is a thing now, so the GS/SpS/EK pulls even with pure EA at the 14th level. I'd agree it's still late, but you are getting a significantly better baseline damage output and spell list out of this.
I think that the EA's baseline damage would be better because of his action economy advantage. I'm curious what particular spells for this build you're looking for that aren't on the Magus's list? The Magus spell list is much broader than many people realize. Unless you're looking for 7th-level spells, of course, but I only rarely play in campaigns where those come up.
When I say baseline, I mean before counting resource expenditure. I know the Magus will do better when it uses spell combat and spell strike. But out of curiosity let's do some back-of-the-napkin damage comparison of Gun Training vs Spell Combat/Spellstrike. Using 14th level is probably cherry-picking in favor of the EK (he's at +11 BAB to the Magus' +10), and 13th is probably cherry-picking in favor the Magus (just got a new spell level and improved arcane pool bonus), so let's go with 12th. Both characters have the same BAB (+9), same highest spell level (4th), and I'll presume the EK is only fueling his mage bullets ability with a 3rd level slot (simplifies the comparison since the effect is equivalent to what the Magus is getting from arcane pool). I'm also going to presume that hitting touch AC is easy by this point and everything hits. The math gets more complicated if that's not the case and there's also a subjective risk management component since the Magus has more eggs in one basket (the spellstrike attack roll).
For dexterity score, I'm going to presume the EK has 26 dexterity for +8 damage per shot from gun training. On a rapid shot full attack, this gives +24 damage if everything hits, or +32 damage if you're hasted. Intensified Shocking Grasp from the Magus alone is going to average 35 damage, and that's without even counting the damage of the firearm itself from the free attack that comes with ranged spellstrike. Presuming you can get your firearm damage to around 20 per shot, this puts the Magus' DPR at 37% above the EK's (or 20% if both are hasted). The Magus could throttle this upwards by using more powerful slots, so as long as he's still got resources he's willing to spend he will outdamage this EK build. On the flipside, the EK doesn't even need to prepare damage-dealing spells, he's free to spend all his spell slots prepping buffs, battlefield control, and utility spells.
Speaking of spells (and setting aside utility spells; I'd imagine you probably don't care much for something like Identify or Invisibility Circle) here are a few in the level 1-4 spell range that wizard gets that Magus does not: Protection from Evil, Create Pit, See Invisibility, False Life, Heroism, Animate Dead, and Shadow Conjuration. I'm sure if I trawled over the spell lists I could find more, but these were ones that just came to mind as not being on the Magus list (and weren't utility spells).