Alarm Clock 7 Segment LED display
It's years later but I found the OP useful so here's some more info, on a similar module also salvaged from a clock. It's a common-cathode display which was driven by a Sanyo Semiconductor LM8560 - datasheet still widely available.

Label on the front is WK6052 (c.f. 'YC-60525S 3' for OP). On the back, 'TB 0.6" 12H 01 06' where 0.6" corresponds to the digit height and perhaps '01 06' to a manufacturing date. 12H matches the fact the clock offered a PM LED and 12-hour display - no 24-hour display option - and accordingly the display itself (like the OP's) had connections for digit 1 to segments b and c only.

Like the OP's, common-cathodes pin 1 is shared with pin 29. Common-cathodes pin 2 is shared with pin 26 (c.f. 25 on OP's - 25 on mine is n.c.). Also like the OP's, pins 7 and 8 were shorted off-board but unconnected to anything else; I don't measure any on-board connections to them either but presumably there's something.

Referring to the OP's diagram above: L1 was used as the PM LED; L2 as the "alarm set" LED (lit when the clock's On-Off-Auto switch was set to Auto); L3 and L4 are the colon LEDs (connected in parallel on-board, so they can't be driven independently); L5 is available on the display but was unconnected (n.c.) in the clock.

Using shorthand 'nx' (e.g. 2d) for the anode of Digit n Segment x, the pinout is:

Pin(s)    Purpose

1, 29     Common cathodes for: L1; L3 and L4 (colon); 2d - 2g; 3a - 3c; 4d - 4g
2, 26     Common cathodes for: 1b, 1c; 2a - 2c; 3d - 3g; 4a - 4c
3         L2 cathode
4         L2 anode
5         L1 anode
6         1b
7, 8      ?? Shorted off-board
9         1c, 2e  (N.B. One common LM8560 datasheet incorrectly has 1c, 2c
          in its Pin Assignment diagram but shows correct pinouts in its
          recommended schematics.)
10        2b, 2g
11        n.c.
12        2c, 2d
13        2a, 2f
14        n.c.
15        3a, 3f
16        3b, 3g
17        3c, 3d
18        3e, 4e
19        4b, 4g
20        4c, 4d
21        4a, 4f
22        n.c.
23        n.c.
24        n.c.
25        n.c.
26, 2     (See 2 above)
27        L5 anode
28        L5 cathode
29, 1     (See 1 above)
30        L3 and L4 (colon) anodes