- my first bet is that the blob IC, near the antenna shown in the first picture, will output at one of its pins the demodulated DCF77 signal.
- second bet is the blob IC near the 32768Hz crystal will output a 1Hz at one of its pins
The entire module with blob ICs can be used as a time-base for the rest of the Nixie display. If not, there are plenty of DCF77 decoders for Arduino, so search for DCF77 Arduino receiver, and a part of these will be for a 77kHz receiver (an opamp), not for the digital ready-made Chinese module.
As for the reliability of the reception, it doesn't need to be 24/7. Usually a DCF77 clock only tries to adjusts itself once a day or so, main ticking is based on its internal 32kHz tuning-fork crystal. I live in Bucharest, Romania, at the edge of the DCF77 signal range, and one of the DCF77 clocks I have is able to sync when the antenna is properly aligned relative to the receiver. The other DCF clock is on a wall and it is not able to synchronize (because the ferrite axis, can not reorient the house walls relative to the DCF77 transmitter

).
Even if the reception is not possible at all, there are Arduino libraries to fake a DCF77-like signal, and transmit that at low power, for your own house only. The Arduino library takes the time from Internet, either by LAN or by a WiFi module. For example,
https://blog.blinkenlight.net/experiments/dcf77/dcf77-generator/
Some text notes I've took while I was tinkering with DCF77 a year ago
2023-04-07 19:45, Fri
=====================
- best DCF77 overview so far, from the PTB itself, at 50 years DCF77 anniversary
- http://www.marvellconsultants.com/DCF/PTBM_50a_DCF77.pdf
- DCF77 is a call sign, D for Germany, C for long waves, F for Frankfurt, 77 a number (here hints the frequency)
- 77.5kHz carrier
- amplitude is reduced from 100% to 25% during ticks
- each second tick encodes one bit
- 25% amplitude reduction for 100ms of the carrier means 0
- 25% amplitude reduction for 200ms of the carrier means 1
- the 59th second mark is omitted, to announce the next tick will mark the start of a new minute
- during each minute, the following are transmitted BCD encoded:
- the number of the minute
- the hour
- the day
- the day of the week
- the month
- the year (2 digits)
- all encoded numbers are for the next minute
- see page 12 of 27 in PTBM_50a_DCF77.pdf
- a pseudorandom phase shift keying is modulating the same carrier (usually the phase modulation ignored by most DCF77 receivers), in addition to the AM modulation
And a receiver that can make use of the carrier's PSK:
http://www.marvellconsultants.com/DCF/