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I don't currently have a voltmeter, and I'm not sure fixing the under hood light would warrant the cost of one.
Is there a Harbor Freight anywhere near you ??? Sometimes they have coupons for a FREE (dirt cheap) Digital Meter (Voltmeter, Low Current Ammeter and Ohmmeter in one) with any purchase (they have $0.99 paint brushes and having a few of them around when you need to use an oil based primer is quite handy - no clean up - just throw the brush away). The Harbor Freight meter is not exactly lab grade quality - but for this kind of troubleshooting - do you really care if the meter is off by a tenth of a volt or two ??? Conversely - Amazon typically has digital meters for less than $15. I doubt that the sale is still on - but before Christmas - the local Sears had a Craftsman Digital Meter on sale For $9.99.
For this particular job - you could also use a 12 Volt test light - they typically cost a few bucks at most auto parts stores, but having a digital meter round is handy for misc. troubleshooting.
What controls the hood lamp is a liquid switch that makes contact when the hood is open.
Make sure your new LED bulb works; connect across either the car battery or just use a 9V battery.
I suggest looking at the connector down by the passenger headlamp, be sure there are two contacts and that corrosion has not eaten them gone. I had to replace both terminals in my car due to corrosion. You will really need a cheap voltmeter to troubleshoot this. Harbor Freight sells one for about $5 or if you can get a coupon for a free one. Not the most accurate, but does work.
Leaving the new LED bulb in place does no harm to anything. Most owners unplug the lamp so as to not drain the battery when leaving the hood open for extended times, even if it does shut-off after 5 minutes or so.
What controls the hood lamp is a liquid switch that makes contact when the hood is open.
Make sure your new LED bulb works; connect across either the car battery or just use a 9V battery.
I suggest looking at the connector down by the passenger headlamp, be sure there are two contacts and that corrosion has not eaten them gone. I had to replace both terminals in my car due to corrosion. You will really need a cheap voltmeter to troubleshoot this. Harbor Freight sells one for about $5 or if you can get a coupon for a free one. Not the most accurate, but does work.
Leaving the new LED bulb in place does no harm to anything. Most owners unplug the lamp so as to not drain the battery when leaving the hood open for extended times, even if it does shut-off after 5 minutes or so.
I unplugged mine a month after i bought my Vette almost 15 years ago and never looked back...
Harbor Freight sends out coupons every month and about every 3 months you can get a free DVM with any other purchase. If you buy the meter without the free coupon it costs about $5.