Detecting a DC current
Just to toss in another thought:







simulate this circuit &ndash; Schematic created using CircuitLab

None of the transistors need to be power BJTs; they can all be small TO-92 types (or smaller.) Optimally, it would be nice if they were matched. But I added \$R_4\$ as a potentiometer so you can make adjustments, instead. This also covers variations in your \$R_1\$ value. Nominally, it should be about 20-30% of the indicated value. But your mileage may vary depending on the matching of \$Q_1\$ and \$Q_2\$ and your actual \$R_1\$ value. (I thought about suggesting a BCM62 for matching but then there is \$R_1\$, so I think the potentiometer is useful until you know what you actually need here.) \$Q_3\$ is totally non-critical. I'm assuming there is a high-side switch here, so \$SW_1\$ is there to represent that detail. (Probably fused, too, but I didn't add that.) If you get BJTs that can stand off some decent voltage (like 2N5401), then there's probably no real need for load-dump protection.

I've not gone through this for all the practical details of an automotive situation. It's more a behavioral approach that avoids opamps. It might work okay, as is.



Just for grins, I tossed the above circuit into LTSpice and used the standard BJTs and \$R_4=22\:\textrm{k}\Omega\$ on a lark. The DC sweep came out this way:



You can play with either \$R_2\$ or \$R_4\$ to change the location where the switching takes place.

If \$Q_1\$ and \$Q_2\$ are matched, it won't even budge even if you vary \$\beta\$ and \$V_{BE}\$ over a reasonable range. Of course.. that's if they are matched. Of course it will work fine then. So if you can, pick \$Q_1\$ and \$Q_2\$ as matched pairs such as BCV62 or BCM62. They won't stand off a load dump well. But they might survive it.

Unmatched, and messing with \$\beta\$ and \$V_{BE}\$ (as a function of \$I_{SAT}\$), I get the following spread:



That's with a fair amount of variation on the BJTs. So it's not horrible, so long as you get the same part number. But it may require some tweaking of either \$R_2\$ and/or \$R_4\$ to make it work well for you.



I've added \$R_5\$ to prevent a mistake in setting the \$R_4\$ potentiometer to an accidentally harmful value. The value of \$R_5\$ should be the same as the value chosen for \$R_2\$, roughly speaking. I had imagined using a potentiometer until the right value was measured, then replacing it with an actual resistor. But if the potentiometer is kept, then the value of \$R_5\$  could be a little less than \$R_2\$ (as little as half) but probably shouldn't be more than 25% larger. Somewhere in that range should be okay if the same exact value isn't available.

I've added some possible protection schemes to the circuit. The diode-only would need to be something with perhaps \$200\:\textrm{V}\$ reverse voltage  and at least \$10\:\textrm{A}\$ capability. The downside of it is that the flyback current dies out slowly. And in this case, it might die out way too slowly. The diode+zener combination provides a high voltage so the flyback current pulse can die out more quickly. But both parts must be capable of the same high current potentials and I'd want about \$30\:\textrm{V}\$ across the pair -- so select a zener in that area, if possible. Finally, there are also  automotive MOVs (Littlefuse makes them, for example) which can repeatedly absorb solenoid flyback energy as well. They come in a variety of voltage ratings. Again, I'd be looking for about \$30\:\textrm{V}\$ here.