Sorry to dig up old bones, but this wasn't really answered completely, I think.
To answer the OP, I'd say yes, you can increase your caster level - but only if you make them as, simply, a Wondrous Item. If you're trying to make them as an Eternal Wand specifically, they're sadly limited in their guidelines and it isn't an option by RAW. Feel free to bring the following up to your DM, though.
If you scroll up a little bit from that table I link later in the post, the fourth note below the "Summary of Magic Item Creation Costs" table says that for all magic item categories, "A character creating an item pays 1/25 the base price in experience points."
4420gp (2210x2 for Base Price) divided by 25 gets you and 176.8, rounded down (as almost everything is in D&D) for a total cost of 2210GP, 176XP, and 4-5 days of work, depending on how you read the "1 day per 1000GP in the Base price". I've heard more often that it's rounded up, but I always round it down - like almost everything else in D&D.
Someone elsewhere had once mentioned an Eternal Wand's cost was that of a Command Word Item with X per day use, as per this table.
So, this is what it seems to be:
Spell level * Caster level * 1800 (command word) * 2 / 5 ( 2 charges per day) + 100 (for the crystal rod).
That would mean the prices are as follows, which are the same as they are in the book. Keep in mind, to make one yourself costs half as much as the totals shown below, along with some EXP and Material Spell Component costs.
0.5 * 1 * 1800 * 0.4 + 100 = 460 gp
1 * 1 * 1800 * 0.4 + 100 = 820 gp
2 * 3 * 1800 * 0.4 + 100 = 4420 gp
3 * 5 * 1800 * 0.4 + 100 = 10900 gp.
Hopefully this helps someone still looking for an answer.