I have this Falk Overtype Engine but am not sure what model it is? I understand it is a No. 456/

Looks to be in good shape and runs well.
Base dimensions and boiler diameter would help.
I just checked mine and it's a JF 491. Look at the under side of the base right below the pillar.
That's where mine is stamped, previous owner scratch or sanded it down to see it better.
If unmarked it's more likely Schoenner.
I think it is a Schonenner Model 107.
What are the dimensions of the base?
OK the base is 7 7/8 inches by 5 inches and it is stamped on the bottom with 142.F.
Am I to assume that is the model number?
More likely a part number than a model number. It's a tossup between Schoenner 107_S or Falk 456_S.I'm inclined to think Schoenner lacking any "J.F." on the underside of the base. They are almost identical as Falk took over Schoenner's production.
The "F" could suggest Falk, but not a certainty. May just be a part or casting number.
My Schoenner 107/13 has the 141 F stamp on the underside of the Base.
So perhaps this may be a Schoenner and not a Falk? I suppose if one bought out the other it could be?
If I were to offer this for sale how would I list it?
How about as a "Falk 456? / Schoenner 107?" with added boiler diameter, flywheel diameter and overall dimensions in your listing.
I'm rather leaning towards the Schoenner manufacture, based solely on the firebox's slotted vents, as opposed to Falks more typical porthole vents at this smaller size overtype .... provided of course, that I'm judging the actual size of your engine correctly!?!?
If I were to offer this for sale how would I list it?
Listing it as “toy steam engine” will get you the same people as listing it with the correct manufacturer/model
My Falk has 6 slots in the fire box with 4 round holes under them on both sides.
I don't know, every Schoenner I've seen has like an olive green paint on the base and flywheel.
This one on eBay say's Jean Schoenner J. Falk because they don't know but look at the color of
the journals and flywheel. This is like every Schoenner overtype I've seen.
https://www.ebay.com/itm/364516609738