Redhawk firing pin question

I have two suggestions. The easy way would be to change out the hammer spring for a heavier spring to give a bit more oomph. It will effect your trigger pull weight to the heavier side though, and wouldn't be my first choice.

This second suggestion is to make it more efficient by polishing some of the internals. Look at your 2nd picture, of the hammer. Do you see the rub mark? You will clean that up with some Mothers Mag or Flitz, and look at the slot for the hammer and see if there are burrs, and clean that out too.

Disassemble the revolver and look for more wear marks, and smooth those out. You arent really removing metal, just polishing it up. Dont mess with the sear angle or any of that though, just the firing controls where it is rubbing on the frame or rubbing where its not supposed to do so. Your firing controls are more than likely broken in to each other.

It will take longer but you'll have a more efficient machine, a better trigger, and hopefully it will clean up your light strikes.

Maybe I'm missing something, but in your top picture the transfer bar is preventing the firing pin from protruding through the recoil shield. So, the revolver will pass the "hammer drop" test.
When the hammer is cocked, the transfer bar drops down and will allow the firing pin to meet the primer and the cartridge will make a bit of noise.

Another thing I would do, because you write that this revolver came to you used, is replace the hammer spring. Who knows how many times that hammer was cocked and fired?

This has been a well known issue with the Redhawk for a long time. It can be firing pin, transfer bar, shooter induced, or a combination.

Out of production does not matter in this case. The Redhawk 44 is still in production and the firing pin will be the same for a 44 or 41. There are two versions of the firing pin. The older has a pressed in bushing while the newer has a threaded bushing. Yours appears to be the older style from what little I can see in the photo. It is fairly common for the firing pin to be too short right from the factory. Have you measured the firing pin protrusion? Just because it sticks out doesn't mean that is enough to get the job done. You need to remove the cylinder for access, reinstall the trigger housing, and measure with the trigger pulled/hammer down. You can use a zip tie to temporarily hold the trigger to the rear. Use stacked feeler gauges to measure the protrusion if you don't have a firing pin protrusion gauge.

Headspace and endshake need to be checked, too. Not likely to be an issue, but it does occasionally happen.

Replacing the hammer spring is a good place to start. One of the biggest issues with the Redhawk trigger quality is that the hammer spring is also the rebound spring, preventing you from soing much to lower the trigger pull without major modifications. Lighter than stock or modified hammer springs are not always to blame, but they are often a problem if there are any other marginal issues with the gun like draggy parts or a minimum spec firing pin. A heavier than stock spring is often called for.

Cleaning up the surface finish of the parts will reduce energy robbing drag and can produce a good bit of improvement in the feel of the action. Just don't get too crazy with it. You do not want to reduce bearing surfaces. Stoning and polishing always remove metal. It can range from insignificant to part destroying depending on the specifics of the required fit. Do NOT stone the lower part of the hammer around the pin hole. Go very lightly with a good stone in the frame's hammer slot. You just want to knock the tops off any rough spots. There are shims available to go on either side of the hammer that, if needed, work well to center the hammer and reduce friction with the frame.

Trimming the hammer nose is a technique that I have used with good results. After truing the transfer bar to remove casting ridges and maximize the impact patch I reduce the nose to the same thickness as the transfer bar. It is critical that it be no less than the thickness of the transfer bar! I like to put a small chamfer on the top edge of the transfer bar, but make sure that the transfer bar is fully covering the head of the firing pin first.

The transfer bar is a known trouble spot, too, at least on some of the newer ones. They can be too short and have minimal contact wit the firing pin. See above.
A new factory transfer bar is available here - https://www.brownells.com/handgun-p..._1=Ruger__Red%20Hawk&avs|Manufacturer_1=RUGER

Rim thickness spec for both .357 and .44 is .060". Most are under that by a little. I do not have published headspace specs for the Redhawk, but use the .357 spec on mine and others that I've worked with no issues. That is .060"-.066". You can measure the rims of a few cases, stick them in the chambers, and measre between the rims and the breech face with feeler gauges to verify your headspace.

I did a trigger job to my redhawk and installed shims. Then I tried reduced weight springs. I got down to a 12lb mainspring functioning in DA 100%. Let the gun sit in the safe for a while and the spring took a set. Then the DA wasn't 100%. Instead of moving up to the 13lb spring, only to potentially have the same issue, I re-installed the stock spring.

The trigger is still very smooth after the trigger job, but it ignites reliably. If the stock spring isn't doing it for you, Power Customs sells a heavier than standard spring. With a trigger job to smooth everything out, you may not notice the extra weight too much.