Engine reads 13118977. Has some pitting. A little hard to
read. Frame is clearly stamped 13119977. The discrepancy
led me to look very carefully at both. No question the frame
number is 13119977, but the 5th digit in the engine number
looks convincingly to have a pinch in the arched right side of
the number, suggesting either a 3 or an 8, looking more like
an 8 than a 3, with what looks like closed loops on the left side.
It IS possible that pitting has caused a 9 to look like an 8, but
it looks more like an 8 than a 9.
A cursory interweb search says both numbers fall within the
range made in January 1926. What am I looking at here ? Is
it unusual for an engine number to be one number off from the
frame stamping ? Would a frame number overrule a non-matching
engine number like this ? What day would it have been built ?
I’m no expert by any means and alot can happen in the course of 90 years of a vehicles life. But if your numbers are that close in matching, I would have to believe that 8 you think you see is really a 9 that matches the frame. That was the idea of stamping both engine and frame.
Now is it possible that they could be off and just by a little bit as you note? Well, anything is possible. But your talking now about an earlier engine finding its way into your frame. That obviously could happen if there was an engine failure and someone found one in a wrecking yard or what not. But the fact they are so close in the number sequence to me says that is not possible–that would be almost as good as coming up one number short in the lottery.
So to me, in my opinion, I think it is very likely your engine matches your frame. Or on the other side of the coin, the frame was mis-stamped by that one digit.
Have any clear pictures of both numbers?
Sure, I can get good pix. But it seems a moot point. The frame number
is crisply stamped into an unpitted frame surface, so it is unmistakable as
to what it reads. The numbers are obviously stamped with an old style
font and I see no reason to question them as being original to the frame (not
restamped). The engine number also looks like all other T engine stampings
for font and placement, … the surface is just pitted.
Am I correct in thinking engines were built and stacked up for installation
in whatever vehicle came down the line. When placed in the frame of the
new vehicle, a line crew member would then stamp the number they saw on
the engine onto the frame to match ??? Or was it done the other way around ?
I suspect someone just goofed and got a number wrong … either both are
original and the framer stamper got a 9 in the place of an 8 on the production
line, or the engine was replaced later with a blank and when stamped to match
the frame, an 8 got mistakenly used where the first 9 was supposed to be ?
Your last statement is what I believe happened…one of those two ways.
Oh great ! … another Model T “mystery” !!! 
So, to the last question … if one were to look for an actual date
these two numbers were produced - nailing down the two days this
vehicle would have been mf’d., … where would I look for such intel ?