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I replaced my power steering pump on the kid's 06 TSX about 18 months ago. It was leaking; but, not enough to drip on the ground. He didn't even notice until I asked him when was the last time he checked under the hood. Purchased an used pump from an 07 TSX with 70K on eBay for $100 and local shop to replace. About 2 months ago, the steering rack was pouring fluid out of both boots. Since it was the kid's college car, I don't know if it started out with drips like yours or straight to failure. Purchased a new rack on Amazon for $240 and local shop to replace for another $250 (install/alignment).
I would check around the pump and rack for oily residue. Might even power wash the area to see how bad it leaks over time. My 08 RDX with +155K power steering pump had a lot of oily dirty build-up around it. Power washed area to check it out over time and it hasn't accumulated any dirt/oil after +8 months after washing.
I think it's coming from one of those metal line fittings.. no leaking near pump or axle boots. can just the line be replaced rather than the whole rack assembly?
It is just so difficult to tell from these pictures. Maybe the lines are just a little loose and need to be re-torqued? Don't have a lot of experience with Honda/Acura power steering. The TSX pump/rack failures with the first I've had since owning nothing but Honda/Acura since 1990 all driven +150K. Might need a shop to raise the car an check out. Might only cost you 1 hour of labor for piece of mind.
The power steering fluid can get thinner if it gets too old, dark, and dirty with contaminants. Fresh PS fluid might also fix the minor leak issue.
Highly unlikely it is the coming from the tubing fittings unless you just installed a remanufactured rack. That does look like PS fluid. I had the same on my 05 TSX 3 different times 1) rack failure ( you will see reservoir drop & accumulation in boot eventually) 2) PS pump leaking at seals (fluid travels to lowest point and accumulates to drip...nearly invisible above that) 3) Pressure side O-ring leak on PS pump top (foaming PS fluid in reservoir overflows and migrates invisibly to undercarriage)
Make sure you monitor the leak. If it gets to the serp belt it will destroy it and possibly leave you stranded with an overheated car breakdown if the wife keeps driving it in the summer heat even after she hears it rip to shreds beating on the underside of the hood. I am experienced in this matter unfortunately.
It seems to me that a TON of ppl have had leaking racks on 04-07 TSX (feel like most have been either 05 or 06). I know mines an 05 and has needed a rack since 2011. I've been trying 2 fig out a way to contact large#s of 1st gen TSX owners & ask whether they've had issues with their rack leaking to find out just how common this issue is.
Also anyone who reads this who has had a leaking rack in their TSX PLEASE go to NHTSAs site..national highway& traffic safely admin...& file a complaint about it bc the more ppl file complaints the better & could easily cause Acura to recall the rack (which in my opinion should have been included in the ps hose recall) & those of you who have already paid to get a replacement would get refunded!! Every single complaint counts! Have your vin# handy before going to the site btw. Here's a link talking about how seriously this org takes peoples complaints so don't just not file one thinking your once complaint won't make a diff!!