N64 RF Modulator/RF Switch Incompatible with Newer TVs?

I just bought a used N64. When I turn the system on with a game in it, everything is fine except the TV screen flashes about twice per second and a clicking sound comes from the speakers (exactly like this).

It did not come with the typically included RCA composite video/stereo audio cable (similar to this). Instead, it included a "Nintendo64 RF Modulator" (model NUS-003) and an old-school Nintendo RF Switch (model NES-003). Our TV is a Panasonic Viera TC-P42S30.

I have tried the following:

• Jiggling all the connections
• Re-seating the jumper pak
• Trying both of the games I purchased with the system
• RF Modulator switch and TV on channels 3 and 4
• Blowing out the game cartridge connectors on the games and on the deck and cleaning them with rubbing alcohol

According to the YouTube video description, the guy who posted it also had his system hooked up via an RF modulator (and presumably an RF switch). He claims one must purchase a proprietary cable from the TV manufacturer to solve the problem. I doubt that. I think replacing his RF modulator rig with something else was probably what fixed it for him.

Could it be that the RF modulators or RF switches just do not play nicely with newer TVs for some reason, and if I buy an AV cable the problem will be solved?