shouldn't really matter which side you stick the DVM, I would just pop the earth terminal, ideally get a second pair of hands, and making sure your DVM leads are plugged into the DVM current sockets and set to at least 1A range, stick it between battery and lead, should not be anything spectacular happening, if you had a passive draw of amps rather than milliamps something would be getting warm.
When you disconnect the battery have you noticed it sparking, that would indicate a reasonably high current draw but nowhere near 10amps. if you were drawing 10 amps not only would your battery be flat as a pancake in less than 4 hours but cables would be noticeably hot, if you want to be really safety conscious try to work outdoors or at least with battery area of car by open garage doors,
once you have a current reading divide it into the battery amp/hr value to see how long before battery goes flat
so if 1 amp and 40Ah battery would last 40 hours
if 500 mA then it would be 80hrs
if 250 mA then 160 hrs
etc etc
you may find this useful ignore the bit a "keep alive memory"
just as an example my V8 quattro drains an 80A/hr battery in around 14 days if I don't use it, bloody modern computerised cars, which is a pita if i go on holiday, (so I have fitted a battery disconnect sw ).
from this I can infer that the ignition off parasitic current is 14x24hrs =336hrs /into Ah of battery
Battery is 80 Ah so 80 / 336 = .238 A or 238 mA
hope this helps
I am around most of tomorrow if you think talking things over would help feel free to give me a ring on 01434 250017 ( after 10 am would be good 😬)
Tim