I once saw an interview with the belgian PM saying that when king Baudouin died in Spain, the cabinet was paralysed and did not know what to do.
It was the Prince of Liège who had to remind them that he was the legitimate successor.
There have been talks that K.Baudouin wanted his nephew Philippe to succeed him, but, even if that was constitutionally possible, nothing was done and his brother Albert, as the immediate successor, followed him on the throne.
Is this the exception, rather than the rule, in royal succession? I believe that generally speaking, when a reigning monarch dies (or abdicates), the heir automatically succeeds -- even before being officially proclaimed as the new sovereign. Belgium, however, is said to be an exception, insofar as succession is not automatic.
Sometimes it takes a while for the death of the sovereign to be confirmed, or to determine the successor if the first in line is only the heir presumptive, not apparent. Also, in the event of abdication, the successor is not always or necessarily the dynast who is first in the line to the throne. It has been said that in 1936 Great Britain, for instance, it was not clear that the then-Duke of York would necessarily become the new reigning monarch, upon the abdication of his older brother, King Edward VIII. Indeed, there was even discussion of bypassing him in favor of his youngest brother, the Duke of Kent, who was married to the beautiful and highly popular Princess Marina of Greece, and who moreover had fathered a son. Nothing came of these maneuvres; but the fact remains that succession by the second son of King George V was not automatic on the occasion, as would have been in the event that the first son suddenly died.
The situation in Portugal 1910 reminds me of the lost dauphin of France, son of King Louis XVI and Queen Marie Antoinette. In the annals, he is listed as Louis XVII -- but of course, it has always been clear that he was king in NAME only, after the death of his father. Hence, the postnominal number 17 -- despite never formally being proclaimed king.
I suppose this means that it is theoretically possible to be king without actually reigning. Indeed, controversy rages to this day about the exact status of King Louis XIX, who abdicated the French throne in favor of his nephew Henri, the Duke of Bordeaux, less than 20 minutes after succeeding his own father, King Charles X, who had abdicated the throne in his favor.
I know that Otto of Bavaria WAS formally proclaimed king, the day after his older brother (King Ludwig II) died -- in June, 1886. Indeed, the historical record has it that he reigned for 27 years (although being styled with the kingly title for 30). But his entire reign was under a regency -- first, under his uncle Luitpold, then his cousin. That cousin, of course, proclaimed himself as King Ludwig III in 1913, the day after the Bavarian parliament passed a law enabling him thus to do.
Well ... just as it's possible to be a king in name only, it's entirely possible to be a king in every respect but name, as in the case of Luitpold, the Prince Regent of Bavaria (1886-1912). After all, a regent exercises all the constitutional powers and functions of a sovereign ...