"Mother was worried because little Alice was ill, especially as father was away in France."
In the sentence, is "as father was away in France" a reason clause or time clause? Which understanding is more logical?
Excellent question. Sometimes, it can be hard to distinguish the two senses of as:
The police car pulled alongside Alice's car on the highway. Alice's heart skipped a beat as she noticed that she was going 15 km/h over the speed limit.
The police car pulled alongside Alice's car on the highway. Alice's heart skipped a beat, as she noticed that she was going 15 km/h over the speed limit.
In the pair of sentences above, (1) invokes the simultaneity meaning of as, while (2) invokes the causal meaning. The difference is as subtle as a comma, so the distinction might be open to interpretation, especially in spoken language.
(In practice, leaving the ambiguity unresolved is not as problematic as you might think. The sentence consists of two statements joined by the conjunction as. As in science, humans often need to consider whether a causality link exists between two observed events. The language merely mirrors the difficulty of interpreting real-life situations, transferring that burden from the speaker to the listener.)
In your example, though, you have an additional hint: the adverb especially makes it clear that as introduces a reason, since it does not make much sense for two events to be "especially" simultaneous.
Here, "as" (one could also use "since" in this case) is synonymous to "because". It is a reason clause.