There is way to get the time information. The way how to retrieve it has some issues but sufficient for your use case, I think.
You can use the TIME variable in the BandMaths and add a band with time information.
This can be done with following graph.
mathTime_and_merge.xml (1.1 KB)
This will give you a MJD2000 time value as double (float64) data type. The data type float64 cannot be used in the GUI, only if you use the GraphBuilder or the Graph XML. This is the first issue.
The time will be the same for each line. It doesn’t check for each pixel. That’s the second issue, but most products only provide start and stop time and not the time for each pixel.
The third issue is that the mosaic processor only handles float32 data. So, you will lose information about the daytime here. Probably it is sufficient for you if you can distinguish between days.
In your case you don’t need the extra graph. You can simply add a variable to your mosaic configuration. I hope this is sufficient for you to distinguish the pixels.
mosaic2_addedTime.xml (1.3 KB)