Len Mason in his book "Using the Small Lathe" gives a sketch of such a tool for the very purpose you require.
I have tried it, and failed. I suspect because my hacksaw blade was not suitable – my so-called cutting corner turned into a nice smooth curve almost before it touched the metal.
What I have done is to take Mason's idea and use it with an old 4" x 1/8" file. The 1/8" or 3.2mm width is actually too wide for my lathe to handle easily so I ground it down to about 1.8mm and this works extremely well up to about 18-20mm diameter parting off. I do use plenty of cutting fluid and a heavy continuous cut.
I did originally have a 1.6mm wide parting off tool which worked well – until I became too ambitious that was.
So yes, narrow homemade parting off tools can be made and will work satisfactorily provide one takes the requisite amount of care.
Have a go – what can you lose?
Regards,
Peter G. Shaw