I was going to suggest that you remove the full diode bridge, and avoid the two diode voltage drops.
Instead put a small bulb for the load. Anything that works on AC. Possibly two led's, anti-parallel. They might light, if your secondary can produce as little as 1 or 2 mA.
You need to match impedance, if you are to obtain maximum power transfer. An led carrying 2 mA at 1.7V, has 850 ohms impedance. Therefore you should make your secondary so it has 850 ohms impedance (or say in a range between 50 and 200 percent of that), at your frequency of operation.
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However since the frequency is 13 MHz, led's may not work.
An alternative source is AM broadcast waves from a nearby radio antenna. 530 to 1700 kHz. They're able to power battery-less crystal radio sets from miles away.