How could you improve entropy on a router running Linux kernel 2.6.x without TRNG or RTC ?
You don't need to continually feed entropy into the system for security, so long as the OS random number generator was strongly seeded once.
If you're unsure about the seeding history of the device, add some entropy. Take a photo of the sky with your mobile phone. Upload to your router and pipe it into
/dev/random. That's all the entropy you'll ever need on that particular device.
Seriously, there is so much nonsense surrounding entropy gathering out there it's almost funny. The Linux manual page for
/dev/random is the cause of much of this pseudoscience; it is simply wrong. The "entropy counters" provided by the kernel are ad-hoc estimates which are meaningless from a security perspective.
You can't "use up" or "lose" entropy on a modern OS. As long as your entropy is used only to seed a CSPRNG (which is true in even very old Linux), 256 bits of entropy is enough for every possible use case. If you don't believe that 256 bits is enough to generate a infinite stream of secure randomness, you'd better stop using AES in counter mode for encryption as well.