I'll continue here my investigations about K101 relay.
Thought it all over:
I also found strange thing. When the coil voltage (current and magnetic flux) decreases, the contact resistance does not remain constant. As the voltage decreases, contact resistance increases to hundreds ohms or 3K-7K until it release. Also when coil operated at higher voltage it makes resistance much lower. Of course, relay is clearly faulty. There should be almost no resistance at all. I thought the problem was in bad solder joint, not reed switch contacts (same as here). Now I'm not sure. How bad solder joints would depend on magnetic flux? And if the reed switch itself is faulty, then it's a fiasco. Even if I disassemble the relay, it won't help.
It turns out, reed switches contacts just oxidized. Reed switches sealed hermetically. It would seem that they should not oxidize. But practice shows that this is exactly what it is. Yesterday, I tried to control relay coil from 30 volts DC. This shouldn't scare anyone because the coil has a resistance of 500 ohms, so the current is 60 milliamps for 1 sec. I heard before that for microswitches and buttons there is such a thing as minimal current. In correct circuit design (as for microcontroller circuits) you must maintain a minimum current so that it breaks through the oxide layer of the contact. Otherwise, the contact stops working over time. I think this is exactly what happened here inside the HP 34401a.
So yesterday I read the datasheet for the relay, installed a light bulb, looked at the current on the power supply, and started passing current through the reed switch contacts, controlling the coil from 30 volts. Then I disconnected the wires and checked the resistance of the reed switch contacts.
I thought that it would be correct to control the coil with one or the opposite polarity. For this, a controlled transistors bridge needed (or a computer-controlled power supply). In theory, just need Increasing the current through contacts and to measure voltage drop across reed switch plotting graph. All this must be done by sending pulses through coil so it clicks contacts hard enough. I think even +/-50v is ok (ten times more, 100milliamps but this just short impulses, not holding current). The main task is to clean the contacts, to remove a very thin layer of oxide. And when the graph becomes +/- flat, it means that the relay is cured.
The 34401a can be used without K101. It does not pass the test with a shorted relay, but other is ok. It seems K101 only function is to completely disconnect de-energized 34401a's input. Not sure if I'm right.
While I was thinking this, an incident happened. My power supply has two channels. There are two double wires coming down from the shelf above. As a result, I applied 30 volts to the relay contacts, but a limited current of 0.5 amps (by power supply current limiting). According to COTO 3501-05-511 datasheet, switching current 0.5 amps, so if HP custom relay like COTO 3501-05-511 it should withstand 0.5amps. But I discovered that the light bulb was now constantly on, contacts were welded to each other. I wasn't too upset, since the relay seemed hopelessly broken to me anyway. However, since there is nothing fragile inside, just reed switches in the filling, I took and lighyly hit relay both sideways and vertically on ceramic tiles floor. It started working again. After this incident when it closed it shows same resistance 213-216 milli-ohms. It doesn't float like it before. However, when I close and open the relay contacts, It can be different each time within a small range of 1-3 milliohms. I don't know if this is normal. Maybe new relay should always have a strict constant resistance? Common sense says that it seems to be. It would be great if someone studied behavior of their new and not new reed relays. We need at least a few of them to accurately determine behavior. Why do I have doubts? Because internal 34401a ADC input is high-resistance, so change in resistance by ohms will be unnoticeable. This only becomes noticeable in a 2-wire resistance measurement. This is my assumption. Having also studied these issues, I believe that the aging contacts of reed relays in precise 6.5 - 8.5 digits instruments is the cause of various kinds of troubles including long-time stability.
By the way, I think Panfnutiy here is incorrect:
Recovery of the relay K101(0490-1914) in HP/Agilent 34401A He tested the reed switches, but he did it with a powerful neodymium magnet. This is incorrect. In my case, relay contact resistance changed when I applied 5V it became significantly less for 30V, vice-versa. Contacts resistance depends on the magnetic flux created by the relay coil. With a powerful magnet it will certainly work. So it is unlikely that the Panfnutiy cause was poor soldering contact. The reason was the same: formation of "something" (oxide, ultrafine powder due to wearing, etc..) on the reed switch contacts. One of the reasons why these relays behave poorly is the low voltage of the control coil. More precisely, high coil resistance (500Ω) and very low current <10mA. It is clear that the coil heats up very little and therefore the thermal EMF is small. But magnetic field is very weak and the contacts apparently are not cleaned properly. They just don't press together hard enough.
For now I soldered the relay back, I want to see how it behaves. Of course, I plan to find a replacement for a new relay. The only reason that made me do all this is the price in local stores, which is from a third to half the cost of the multimeter itself.