History of the train boards above the ticket windows:
Prior to 1967... no departure boards in a central location. Individual boards at track gates with roll signs. Space over ticket windows used for advertising. You probably had to ask at the ticket window or info booth to find your track number, or just stroll the concourse looking at the over-gate or under-balcony indicators.
Solari boards were put up in 1967-1968... one for NH, one for NYC, both mounted over NYC ticket windows. No boards over NH (east) windows.
After the PC takeover, the NH board became a board for New Haven Line trains, the NYC board for Harlem-Hudson Line trains.
Sometime around this time, the overhead gate triangular indicators had their "destinations" removed and just "TRACK ##" inserted. A whole array of these were mounted underneath the balconies to accommodate those tracks not in the main concourse.
Later, in the 1980s, 3 Omega boards installed. Similar to the Solari board, but there were now 3... one for New Haven Line departures, one for Harlem-Hudson Line departures, and one for "All Train Arrivals". Survived until c 1997.
During the GCT 1996-1998 restoration, the LCD boards were installed (the ones that were just replaced with the digitals). This brought about the first time ever that a departure board was placed over the former NH ticket windows. 3 boards given to New Haven departures and 1 general information board. Over the active ticket windows, 2 boards for Harlem, 1 for Hudson, 1 for general info. Train arrivals moved off the boards and onto a computer monitor at the info booth.
The New Haven Line is IIRC the busiest commuter rail line, and, as mentioned above, during rush hour/peak hours, there are numerous departures within a 1-hour period, all to various destinations.