short circuit , or the battey needs replacing it may not hold a charge
Then replace the battery.
on mine, the drain hose is connected to the battery tray on the left side of the bike. ( look for a hose under the battery tray, remove the hose clamp to disconnect hose and drain oil )
Ground it to the vehicle frame or engine.
down on the passenger side engine or follow the positive side on your battery
It arcs because something is on when you installed the battery. Can be a light, or relay sticking.
Anything below .030 A is normal.
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Weak or bad battery? Does not hold a charge? Excessive parasytic load? Hidden drain on battery i.e. trunk light on, glove box light on, underhood light on?
On a 1991 Miata, the battery is in the trunk. It is probably the same on the 1990.
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We need to know which drain plug you are referring to, there are several.