via a RS-232 phototronics serial port at the back, according to the manual
The manual may be a bit loose with its terminology.
RS232 defines the ELECTRICAL interface, the voltage levels and also the connector, it does not define the format of the data on the lines.
99.9% of the time the data format is asynchronous serial data, but not always.
The cable (which you don't have) for the multimeter obviously has some electronic circuits in it to convert whatever comes out of the photo transistor to voltage levels.
Looking at your oscilloscope waveforms, I am not sure that you are seeing the correct waveform, it could be that the sampling speed is a bit low, hence the fast pulses are one height, and the slower pulses are of greater height (in the negative direction) (I know what I mean!
).
Try speeding up the sweep if you can on that scope and scroll through the data stream rather that trying to put it all on the screen at once.
As a way forward in decoding this data stream, can I suggest that you:
Set the meter so that the display is all zeros.
Change the mode, ie DC volts, AC volts, DC current, AC current etc and see what changes in the data stream.
Now try changing the range and see if there is a change in the data stream. The decimal point should move.
Inject a voltage and change the digits one at a time, again looking for where the change is in the data stream.
While doing all this, bear in mind that if the output is "RS232"
for display on a PC or whatever, it will probably be coded in ASCII,
also, on the scope screen, the most significant bit of a byte of data will probably be on the right of the group with the least significant bit on the left.
Not MSB on the left and LSB on the right as it is usually displayed on the written page. (I have burned my brain with this many times over the years).
JimB