Signal bridges were usually numbered west to east. Automatic block signals (and distant signals) were usually numbered to the nearest milepost and all originally had a prefix letter for the branch, as follows:

A-Atlantic
B-Bay Ridge
C-Central
E-West Hempstead (NY Bay Extension RR), no automatic signals but a few distant signals.
F-Far Rockaway
G-Main Line (later, no prefix letter)
H-Hempstead
M-Montauk Cut-Off
Smash board and eastbound Signal #006 at Dutch Kills Drawbridge (swing bridge). 
 View southeast at Dutch Kills 06/1981  Photo: S. Goldstein

N-Port Washington (North Side)
O-Oyster Bay
P-Port Jefferson
R-Rockaway Beach
S-Montauk (South Side RR)

For example, signal S243 would be nearest to milepost 24.3. Also, even numbered signals are usually eastbound and odd numbered westbound.  Info: Jeff Erlitz

Amityville-Copiague-Lindenhurst was the "test site" for no wayside automatic block signals. It was probably designed in 1968 or before since the shoo-fly tracks for this section were placed in service in October 1968. I'm guessing that the railroad did not know for sure that the FRA, or whoever, was going to approve the use of no wayside automatics so they designed the new elevated with the provision for them. This was the first section of railroad to operate under Rule 410.

The following year, in May 1974, the automatics came out of service from Queens to Divide and in November 1974 from Hall to Queens.

Oyster Bay Branch, Montauk Branch from Babylon to Y and west of Jamaica are the last bastions of automatic block signals, Rule 251. Of course, the Main Line west of Jamaica also but that's not 251 territory.

The Central branch still has its automatic block signals, such as C229 distant signal to Beth. It's your basic Rule 261 automatic block signal system with out speed control. The automatic block signals for the Atlantic branch between Hall and Valley were replaced in the late 1990's, about the same time Hempstead branch automatic block signals were replaced.

Far Rockaway Branch lost its automatics 2/4/1984
Long Beach Branch lost its automatics 12/2/1982
Hempstead Branch was after 1990  Research: Jeff Erlitz
 

Bellerose Signal H-140 8/1967
(Brennan-Erdman)

Looking west on Line 2 in F Interlocking, LI City.
Home signal 708W on the right and 704W on the left.
The Line 2 Connection track is coming in on the left.
Info: Jeff Erlitz
 

Bellerose 2/14/2008

JS interlocking east Deer Park

PD in service 4/27/2006 Photo/Archive: Nick Kudrey

LIRR new signal installation Patchogue 
4/29/2006 Photo: Paul Strubeck
 

West end of Dutch Kills Drawbridge looking west

View west at the former Farm 1 Interlocking,
just east of Farmingdale station
 

M7 #7199  Train #9713, one of the "extra" Hempstead to Penn Station trips that operate on the "MLX" weekends when there is no service on the Main Line between New Hyde Park and Hicksville. View E at Signal Bridge 3, Queens Interlocking west of Bellerose station, on the border of Bellerose Terrace (on the left) and Elmont (on the right). 10/24/2021  Info/Photo/Archive: Jeff Erlitz
 

Cannonball westbound under signal bridge #18
LI City  05/11/2010 Photo: Joe Tischner
 

1st signal: unidentified
2nd signal = #18
3rd signal  = #N18  (Port Washington Branch)
4th signal  = #NY248 (NYCRR)  

Signal bridge #18 east side of “HAROLD” tower (or where HAROLD used to be) at the loop tracks leading into Sunnyside yard, close to 42nd street in Woodside, Queens. Research: Dave Keller

(ABOVE) Looking west towards New York, left to right:

Track 4 (eastbound local Main Line): red over red (wrong way)
Track 2 (eastbound express Main Line):  red over red (wrong way)
Track 1 (westbound express Main Line): yellow over green, diverging route to Grand Central
Track 3 (westbound local Main Line): green over red, through route to Penn Station
Port Washington eastbound track: red over red (wrong way)
Port Washington westbound track:  yellow over green, diverging route to Grand Central      Info: Kevin Wong
 

LIRR refers to them as a “Low Home” signal.  “Low” because it indicates “slow/restricted speed and unless otherwise posted is displayed lower than pedestal/full size position light  signals.  “Home” because they display the most restrictive aspect of Stop Signal.  All “Home Signals” per definition on the LIRR display “stop signal” as their most restrictive aspect.  On the PRR, Amtrak and NS these signals are referred to by the PRR jargon of “Dwarf signal” and Low Home/Dwarf signal are used interchangeably. 

The reason for the silver back was to make the back side of the signal clearly distinguishable when running against the normal direction of traffic.  The signal indicated in red is illuminated west and therefore
it would be governing eastward movements from Richmond Hill (receiving yard) going east protecting the ladder (double slip switches).  5/2023  Info: Joe Vila

Jamaica HALL - Dwarf  Interlocking Signal 12LB old style PL-4
11/04/2023 Photo/Archive: Thomas Farmer

HALL Interlocking Dwarf Signal 12LB - 6/01/1993 Archive: Jeff Erlitz