the front of my pick-up is according to "myth" originating from a 1919 touring, where the rear has been cut off. Standard recycling of a Model T back in the time when living on a farm.
It was obviously a non-starter touring as the ignition switch sits on the coilbox and the windscreen frame have integrated brackets for sidelamps.
Was there no dashboard in these non-starter cars?
From the photo in your profile, the red cutoff touring appears to be a USA body -- i.e. the left side door is a dummy/false door.
You asked, “Was there no dashboard in these non-starter cars?”
The answer for the USA non-starter open cars is they did NOT have a dash panel (the metal part that fits just below the windshield and holds the ignition key – see Lang’s TM-201 at: https://www.modeltford.com/item/TM-201.aspx ) until the switch on the coil box was deleted from all production during 1922. When that occurred, for non-starter cars the ignition switch along with the headlamp resistance coil was mounted to metal dash panel. For the starter cars they used the same dash panel but mounted the ignition switch and amp meter in the pane.
Note Ford called the wooden and later metal firewall a “dash” so we are not talking about that one.
From Bruce’s on-line encyclopedia at: http://www.mtfca.com/encyclo/C-D.htm#cb1 he has the following about the coil boxes:
Part # Factory #
4725........1383.....Ford. Non-starter cars. The same as in 1918.
4725B ----- .....Ford. Starter cars (no switch on box).
5000....1383....Ford. Same as 4725, non-starter cars.
5001....1383B....Ford. Same as 4725B, starter cars.
5001....1383B....Ford. All cars (switch was on dashboard)
Note if you are not talking about a USA open Model T then, please let us know what country produced the body and chassis. I would guess, but it is only a guess that they are USA parts assembled somewhere in the world. I don’t think that will change the answer, but I have not checked that either.
Hap l9l5 cut off
Non starter cars had no dash board until 1923 models, and even then the steering column bracket had not been introduced.