help installing nut on brake booster pump

I managed to remove my 2010 Prius master cylinder. Now I am removing the booster pump. The 10mm nut on the end of the pump is a problem for me. It is the nut closer to the firewall. I broke the nut loose and I can get only one finger on the nut to unscrew it, but not hold it. Maybe I have big hands. I was about to unscrew it and hold a magnet close by when it falls. Then I thought about installing the nut later. I removed the nut for the nearby wire harness bracket, but that did not help. Youtubes do not show how it is done.
Any suggestions or ideas?

 

Thanks. I did get it out and surprisingly, I did not drop the 2 nuts. I do not look forward to intalling it. Maybe I can push the pump to the left and that will give me maybe 1/4" more room. Youtube makes it sound easy. They do not show them doing it.

 

Thank you for your reply.
The problem is getting my fingers onto the nut. I would have the same problem getting my fingers on a socket. There is no room for an extension or rachet. I removed the pump, finally. Youtube states to use a crowbar to shift the pump to the left to unhook from the mounting pins. There is a bracket blocking movement to the left. I had to use enough force to flex the bracket. I will bend it before installing the new pump so that it will be out of the way.
I was surprised that others have not posted about this difficulty. I will post a comment on any tricks putting it back together.

 

Old part number on new pump.
Thanks. Useful advice. I will magnetize a screwdriver.
I opened the boxes with the new brake parts. I found that the part number stamped into the pump casting is 47070-47050. This is the old part number. It was superseeded by 47070-47060. There is no part number on the label. My invoice lists the new number and the new number appears on the outside of the box. The Toyota dealer said that they sent me the new part but Toyota continues to stamp the old part number on the casting. This is surprising. The main visible difference is that the new label is white while the old one is yellow. Both labels are orientated sideways.

 

I dropped a rubber mount. Then I took the rubber mount from the left hand end of my old pump. And dropped it, too. I spent 90 minutes trying to find either one. I bought a large hand mirror, jacked up the car on both sides, removed one wheel and used the flashlight and mirror to be sure that it was not in the grass. I dropped a wad of paper to see where it ended up, but it landed in the grass. Then, I used an air hose with a 12" long nozzle to blow air everywhere I could. I think it fell into a black hole. I finally found a rubber mount under the steering box. There is a bowl shape there where the contents cannot be seen. So, if you drop something, remove the driver's side tire and check in the bowl.
Tip #2- When removing brake booster and pump, wrap an old towel around it. I did not. see image
When inserting the pump into mounts, the pump wanted to push left. I don't know why. And when I pushed it back, a rubber mount fell out leading to the above problem. I finally blocked it from going to the left with a block of wood. I used wire to tie things out of the way. See images. I almost decided to remove the coolant hose under the EGR cooler, but did not.
I was able to squeeze my hands around cables and use a finger from each hand to get the 10mm nut nearest the wirewall started. My arm is bruised, but I bruise easily. I got the other nut started by using a AWG12 wire bent so that I could place the tip of the wire (with nut) onto the end of the stud on the pump. I used a long screwdriver to rotate the nut. It took patience and luck. See images
So, tomorrow, the booster installation.
Thanks for your replys and advice.

 

The master cylinder was easier to install. I made one mistake; there is a bracket that supports the red brake line next to the M/S. The bracket is bolted to the M/S. I removed the bolt holding the brake line to the bracket instead of removing the bolt holding the bracket onto the master cylinder. Installing the wrong bolt was difficult.
Now, I will bleed the brakes. I am buying Windows XP 32 bit to downgrade my laptop.