The almost certain answer to your specific query is: "No, but it may work with modifications."
(More about that later ... )
In the mean time - here's the most straightforward approach if you really want to use all OEM components ...
The white-faced gauges were only available on a 2004 Regular Cab / XtraCab 2RZ 5-lug minis as part of the following option packages:
SR5 Chrome Package
SR5 Color-Keyed Package (Available in Lunar Mist, Black Sand Pearl, Radiant Red and Impulse Red only)
If you can find an OEM 2004 5-lug 4-cylinder cluster from a Taco with one of these option packages it should theoretically be plug 'n' play.
These option packages (including the white-faced tach cluster) were available in all 4 years from 2001 - 2004. I can't guarantee the clusters themselves were identical (same part numbers) in all 4 years.
Here (attached) are parts diagrams from the original 2001 - 2002 factory parts listing. I don't know whether or to what extent this listing changed (new / different part numbers) in 2003 or 2004.
You'll see that some components are specific to 4-cylinder versus 6-cylinder models, and some are specific to the tach cluster versus the non-tach cluster. There are even a couple of items that depend on transmission type.
To make the tach cluster work in your '04 Regular Cab 4-cyl will require some surgery and / or frankensteining.
For one thing, you'd have to swap all the gauges. I'm not sure what you'd be able to do about the odometer with trip odo feature. I can't even guarantee the gauges would physically all swap over "as is." (... though I suspect there's a very good chance they would)
There are also wiring differences among models / equipment related to the cluster, so some creative re-wiring may also be required.
BOTTOM LINE: It's gonna take time and effort to make it work. Whether it's worth it just to have the 100% OEM look is up to you. Your best bet (IMHO) is to track down an OEM tach cluster from one of the options packages mentioned above. Otherwise, you can simply add an outboard tach a lot easier than doing all the surgery / retro-fitting it appears this mod would require.
Just my .02 ... No warranties, express or implied ...
So, @Enola Gaia if one were to add an aftermarket tach. What's the brand to run and where do we tap in?
(Why i ask is had a corolla that the tach I got did not work on the wire I was supposed to tap. Ended just not using it and)