The Invercone converts the meter for use as an incident light meter, this will be true for the Master II as it is for all following Masters. My guess is that early manual was not written with the Invercone in mind, perhaps it had yet to be added as an option.
Quality Light Metric in Hollywood still works on these meters, and the price and turn around are very reasonable, exceptional even.
Here's another vote for Quality Light Metrics. They do outstanding work, and the price and turnaround really are pretty reasonable. The meter comes back with a little yellow sticker attesting to the accuracy, exactly as one expects from a professional calibration lab. Of course, if you're not in the US it's probably a little pricey for shipping.
As for the invercone on a Master II, if you look at a Master II and a Master III you'll note that neither of them "indicate" the exposure. The needle measures light, and the readings on the two should match - invercone or no invercone. Mechanically there's no difference between the invercone for a II and III. They are the same part number. It's the same invercone. (Not so for the Master V. Different mechanics.)
What differs on the II and III is the calculator wheel. As someone pointed out earlier in the thread, to get good readings from a Master II just click the ASA rating down one notch on the calculator wheel. That's all that's required.
If you're shooting 100, set the calculator wheel at 80. If you're shooting 400, set the calculator wheel at 320. If you're shooting X, set the calculator wheel one notch slower and read it directly. The point to remember is that the calculator wheel is completely disconnected from the light meter portion. Adjusting the film speed setting wheel has absolutely no effect on the needle readings like it does on the meter on many SLRs. On the Westons the meter needle doesn't read out in exposure times. The calculator dial gives you the exposure times based on the light intensity read form the meter needle.
What I love about the old things is that I can look at a glance and see a range of corresponding aperture/time values in 1/3 stop increments for the light condition.
No, it won't do spot measurements. Use it for what it's good at.
I measure the shadows I want to preserve cleanly, rather than trying to measure the aggregate scene, and I set the exposure calculator wheel Zone 3 pointer to the needle reading based on that shadow measurement. Then, voila, I'm presented with a range of aperture/speed settings that will properly expose those shadows. Use modern film and I don't blow out the highlights.
Works for me. YMMV.