How do I mount the EFI partition on Windows 8.1 so that it is readable and writeable?

The official way of mounting the EFI partition is

mountvol b: /s

where b: is a drive letter of your choosing. You can remove the mapping with:

mountvol b: /d

You still need to launch explorer.exe with administrative privileges in order to see the mountpoint (kill explorer.exe, then launch one from an elevated command prompt)

The reason why you can't access it on Windows Explorer (File Explorer) is because by default it does not run with administrative privileges. If you let's say kill Explorer and execute it again from an elevated command prompt then you will have access to the EFI partition through File Explorer.

First open an elevated command prompt and give the EFI partition a drive letter, you can do it with mountvol as shown in jmiserez's answer (recommended) or with diskpart. In the following example the EFI partition is on disk 0, partition 1 and will be assigned to letter b:

diskpart
list disk
select disk 0
list partition
select partition 1
assign letter=b
exit

Now kill the File Explorer process and start it with administrative privileges:

taskkill /im explorer.exe /f
explorer.exe

Now you can access the EFI partition with File Explorer.

Note that the EFI partition is a FAT32 file system partition. FAT partitions don't have the Security tab, this is a NTFS feature only.

One way I found is to open it in the administrator command prompt:

type E: then you can browse around and edit the files