New to my Esprit V8, so this is more a question than suggestion based on first hand knowledge.
I notice for the Esprit when you disconnect and reconnect the battery, the headlight pods cycle up and down once. I understand from archive posts this is normal on the Esprit. Sort of interesting behavior. Haven't looked into the wiring details yet. Pretty familiar with pod motor wiring options from adding them to my '69 Plus 2 to ditch the stock vacuum pods, and know some configurations can result in a parasitic drain. Wiring configuration I used has no drain and does not cycle like this, although it does not provide a 'Flash to Pass' feature.
Anyway, my question / concern... Might be best to check and remove the fuses controlling the pod motors & headlamps first in your checking sequence and eliminate them as a parasitic drain issue? Thought is that with your Ammeter set to (presumably) mA scale and in series with the positive battery post, you might fry the instrument if the high draw of the pod motors and headlamps kick in while fiddling with fuses and connection / disconnection of the battery?
As a go-by, my '87 BMW has this sort of constant battery drain, and it is completely normal at about 50 mA. This generally results in flattening the battery in about three weeks. No alarm, but remote locking.
Anyone got the normal constant draw for the Esprit handy? Is it generally around the 50 mA level?
Assuming some level of parasitic current is normal on the Esprit, you had a second question on options to mitigate. Again, for my Plus 2, I installed a remote controlled master shut-off switch on the positive battery terminal. This disconnects everything. It is on the positive side so that the internal latching relay is supplied with power. The remote is a key ring fob. A latching relay has no draw in it's 'latched' position; it only needs power when you engage or disengage it. The one I used is called a BatteryBrain; I think there are other brands available in the marine electrical world.
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I really like this set-up as the Plus 2 battery posts are buried under the trunk floor, so was a hassle to disconnect while doing service work. Disadvantage of this set-up is depending on the radio you have you may loose your pre-sets every time you turn it off; my Plus 2 radio has permanent memory so not an issue. Manual shut-off switches are common as well; similar but generally mounted on the ground side.