This what the old-timers called a "Modulator", or "Modulation Box", or "Swing Box". I remember hearing this design called a "Mule Box" because of how your wattmeter would "kick like a mule" when you speak.
Never have found out how the term "Jewel Box" got associated with them. Maybe because the cabinet is not much bigger than the better half's box of jewelry? Maybe? I'll probably never really know how that name caught on.
I am pretty sure that's what the initials "JB" found on Black Cat amplifiers is supposed to mean.
The tube is biased way below cutoff. This permits you to use a much higher power supply voltage than the tube would normally tolerate without immediate damage. A PA amplifier meant for a high-school gym in 1955 might use two 8417 tubes running at 450 or 500 Volts. The JB150 puts 800 Volts on the tube's plate circuit. This vastly improves the tube's peak-power output.
Your carrier is only partly amplified, since only the upper part of the carrier's waveform can turn the tube "on". The high negative bias cuts off the lower part of the carrier waveform. But that's not so bad by itself, since the tuned circuit in the tube's output side restores the 27 MHz carrier back to a RF sine wave, more or less.
The real action occurs when you modulate the carrier. The audio waveform is "riding" on the reduced carrier, and gets amplified at full blast, as though the carrier really were turned up to 20 or 30 Watts.
Gives it that "asymmetrical" audio 'swing'. The tube's power gain applied to audio peaks is several times the gain that is applied to the carrier alone. This is where the asymmetry happens, in the tube's grid circuit. Adjusted correctly, the receiver at the other end hears a higher level of modulation than he did from the barefoot radio.
Sure, it's a primitive way to achieve this, but it was cheap and sounded good enough for the old tube operators. And it permitted you to adjust the carrier level feeding into your "big" box down to a safe level that wouldn't melt your 3-500 tubes. Variable "key" on a tube radio can be done, but it's tricky if you want to retain full power on modulation. Turning down the carrier in a tube CB generally turns down the peak power in direct step with the carrier.
Or you could use it to "nitrous" your D&A Phantom 500. Wouldn't wear out the tubes the first day, maybe not the first week if you kept the carrier turned low enough. But the impressive wattmeter readings still took their toll on tube life. But for a wattmeter-worshipper, this was pure gold.
Looks a bit odd on a 'scope, but the base-station operators 40 years ago didn't use one.
Bear in mind that a large radio 40 years ago would bust a gut to show 18 Watt peaks on AM. A typical low-priced tube-type base radio would show a 3 Watt or 3.5 Watt carrier, and maybe 14 Watts PEP. If the final tube was a little tired, an average-reading wattmeter would show backwards swing on modulation. The JB would fix that. This is the drive level that the JB150 was optimized for. The smaller the radio, the bigger this thing makes it become, more or less. A modern radio with more than 20 Watts PEP on AM will make it work too hard, unless it's modified to tolerate more drive power.
But what you're seeing on the 'scope is probably what it's supposed to do.
73