if one was inside the black hole, with sufficient mass under your control, you could pass a signal to outside the hole by shifting the mass this way or that

Wouldn't shifting the mass require pushing against another mass? In that case, might those two signals cancel each other out?

It stands for Laser Interferometer Gravitational Wave Observatory!

The black holes are so big and fast when they spiral in and merge that they literally create waves in spacetime which change the length of things by a tiny amount as they pass by us and LIGO is able to measure when the two arms of it change length by nanometers and that's where we got the signal.

There's also The Event Horizon Telescope which made radio images of the black hole at the center of our galaxy. We haven't been able to catch a merger with this though.

you should really read the Wikipedia article on black holes: https://en.wikipedia.org/wiki/Black_hole

some paragraphs you might find relevant to your question:

By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical Hawking radiation, so astrophysicists searching for black holes must generally rely on indirect observations. For example, a black hole's existence can sometimes be inferred by observing its gravitational influence on its surroundings.

David Finkelstein, in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. The first black hole known was Cygnus X-1, identified by several researchers independently in 1971.

The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Any matter that falls toward a black hole can form an external accretion disk heated by friction, forming quasars, some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed."[11] If other stars are orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.