Depends on a few things as to whether it would be a #2 with reversible firing pin. First off would be whether the cartridge it's chambered for was ever offered in both RF and CF cases. Ballard didn't use the reversible firing pin system if the cartridge wasn't offered both ways. I've owned .32-20 and .44-40 Ballard #2's and all had CF firing pins.
Second would be if it's even a cast steel action or forged steel. I've never seen a forged action with reversible firing pin unless serial numbers didn't match because someone swapped in a #2 breech block.
Almost all cast #2 actions have a 3 line rollstamp on the left side, and forged are 2 line, but there are exceptions both ways. I own a forged Rigby Ballard with 3 line address, and once owned a cast #2 with a 2 line address.
I also own a #3 Gallery that's chambered in .25 Stevens RF, but it's marked under the forearm on the barrel as having been rebored and rifled by J. Stevens A&T and .25 Caliber. So not factory. The .25 Stevens came out after Ballard production halted, so none in .25 Stevens would be factory done.
It's possible it might be the .25-20 SS chamber, and if it is it may or may not be factory original.

Cartridges that were made in both CF and RF are .38 Long, .32 Long, .44 Long. Don't know of any others that were both.

You're welcome.
So do you own this rifle yet, or considering buying it?

I read a mention somewhere that the .25 Hornet was devised as a handy low-pressure cartridge for revamped Ballard rifles that ordinarily might be on the ragged edge for hi-speed .25-20 WCF and .22 Hornet ammunition.

The rifle in question might be one that was rechambered for this reason.

The .25 rimfires by Stevens had a groove diameter of .251.  The centerfire .25/20s were .257.

waterman wrote on Mar 7^th, 2025 at 4:12pm:

That is not correct. It is an often repeated, incorrect piece of information that seems impossible to get corrected. The standard information in cartridges of the world, repeated by wiki and other sources also has an introduction date that is late by 10 years.

Here is a good discussion of it complete with patent drawing from UMC of the long version of the 25 Stevens.
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The 25 pistol cartridge that was introduced in 1860, was .250” diameter.

This help?