That's great progress. 1.08 A is a huge draw, ideally it should be around 50 milliamps or less so 0.09 - 0.11 amps with that fuse out sounds a lot more manageable.
Just to be sure it's the radio, did you try keeping the fuse in but disconnecting the radio harness to make sure the power draw went down?
Installing a fuse won't help with reducing power draw unfortunately, it will do nothing unless the draw goes over a certain threshold and will then "trip" so the circuit breaks and is no longer powered. This protects the wires and circuits from overheating and burning out.
What model head unit do you have? When the cars off it should go into low power mode and not draw that much power. If it's a smart unit you may want to check the settings menu to make sure the option for that is turned on (it could be off so the radio is on full power all the time).
Next thing you may want to look into is that the wire that should be connected to ACC (which is powered off when the car is off) could be wired to a constant power connection instead. This would mean the unit thinks the car is on all the time and keeps everything on it running which would result in a high draw.
If that isn't the problem then the only real solution would be to disconnect each wire in the harness individually and see which one "fixes" the problem. If the only wire that is the culprit is the connection to battery you may want to try divert that to an ACC wire instead (like one from the cigarette lighter connection) so it's only on when the car is on.
If that doesn't work out I would contact the seller you bought the radio off with your concerns. If nothing comes from that then your only option would be to buy a new radio instead.
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I have this sort of radio which is Android based and it correctly goes into low power mode when the car is off and (touch wood) never had any problem with starting the car even after days of no driving.
Let us know how you get on.
Just to be sure it's the radio, did you try keeping the fuse in but disconnecting the radio harness to make sure the power draw went down?
Installing a fuse won't help with reducing power draw unfortunately, it will do nothing unless the draw goes over a certain threshold and will then "trip" so the circuit breaks and is no longer powered. This protects the wires and circuits from overheating and burning out.
What model head unit do you have? When the cars off it should go into low power mode and not draw that much power. If it's a smart unit you may want to check the settings menu to make sure the option for that is turned on (it could be off so the radio is on full power all the time).
Next thing you may want to look into is that the wire that should be connected to ACC (which is powered off when the car is off) could be wired to a constant power connection instead. This would mean the unit thinks the car is on all the time and keeps everything on it running which would result in a high draw.
If that isn't the problem then the only real solution would be to disconnect each wire in the harness individually and see which one "fixes" the problem. If the only wire that is the culprit is the connection to battery you may want to try divert that to an ACC wire instead (like one from the cigarette lighter connection) so it's only on when the car is on.
If that doesn't work out I would contact the seller you bought the radio off with your concerns. If nothing comes from that then your only option would be to buy a new radio instead.

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I have this sort of radio which is Android based and it correctly goes into low power mode when the car is off and (touch wood) never had any problem with starting the car even after days of no driving.
Let us know how you get on.